A piece of ice with a small stone embedded in it is floating in a glass full of water. What will happen to the level of water when ice melts?

The entire system can be imagined as the ice floating in water without the stone and the stone in a massless invisible boat floating on the water. (I) When the ice is floating on water, it displaces a volume of water the mass of which is equal to its own mass. When the ice melts, it becomes liquid water. Upon melting, mass does not change. Hence, volume of this water must be equal to the volume, which was being displaced when it was in form of ice. (II) As soon as the ice melts, the masless boat vanishes. When the stone was floating in this boat, a volume of water was being displaced the mass of which was equal to that of the stone (as the boat was massless). As the boat vanishes, the stone sinks. When the stone sinks in water, it is displacing a volume of  water, which is equal to its own volume. But because of the fact that it sinks, the mass of this volume of water has to be lesser than that of the stone. This implies that the volume of this water displaced by the stone is less than the volume of water displaced when it was floating. So, the water level comes down. By combining the results of both the cases, the water level will decrease.