If speed is relative to the belt, then the plane moves forward on the belt at a rate of 10 knots over the belt, the belt spins backwards at 10 knots, and the plane moves forward just the same. That in turn increases the relative speed of the aircraft. Situation: entirely impossible. Even if it were, the plane would still take off.

You're right when you say the only speed the belt could match was zero.

Still doesn't matter, the plane takes off.

::ETA:: even with constant exponential acceleration of the belt, the plane can overcome the minimal friction of the conveyor under its free-spinning wheels.