YES
O(n^2)
TRS:
 {
       g(x, s(y)) -> g(f(x, y), 0()),
  g(0(), f(x, x)) -> x,
  g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0())),
       g(s(x), y) -> g(f(x, y), 0())
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
         g(x, s(y)) -> g(f(x, y), 0()),
    g(0(), f(x, x)) -> x,
    g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0())),
         g(s(x), y) -> g(f(x, y), 0())
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 0][X1]   [1]
   [s]([X0]) = [0 1][X0] + [1]
   
       [X3]  [X1]    [1 0][X3]   [1 0][X1]   [0]
   [f]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [1]
   
         [0]
   [0] = [0]
   
       [X3]  [X1]    [1 1][X3]   [1 1][X1]   [0]
   [g]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0]
   
   
   Qed