As the time is passing, entropy of the universe

According to second law of thermodynamics, the entropy $${\left( {ds} \right)_{universe}} > 0,$$   for an irreversible or spontaneous process and $$d{s_{universe}} > 0$$   for an reversible process or almost equilibrium reached process. So for a natural process since there will be irreversibility always the system entropy goes on increasing until equilibrium is reached and once the system reaches the equilibrium the system entropy becomes equal to zero. Hence a maximum exists for a system.