YES
O(n^3)
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
       [X2]    [1 1 0][X2]   [1]
   [s]([X1]) = [0 1 0][X1] + [1]
       [X0]    [0 0 1][X0]   [1]
   
       [X5]  [X2]    [1 0 0][X5]   [1 0 0][X2]   [0]
   [f]([X4], [X1]) = [0 1 0][X4] + [0 1 0][X1] + [1]
       [X3]  [X0]    [0 0 1][X3]   [0 0 1][X0]   [1]
   
         [0]
   [0] = [0]
         [0]
   
       [X5]  [X2]    [1 1 1][X5]   [1 1 1][X2]   [0]
   [g]([X4], [X1]) = [0 1 1][X4] + [0 1 1][X1] + [1]
       [X3]  [X0]    [0 0 1][X3]   [0 0 1][X0]   [0]
   
   
   Qed