with no energy source
When changing reference frames
You're making a complete hash of elementary level physics. I based what I said on your diagram, not any 'single medium' or anything else.
There's no reason to change the reference frame at any point here and doing so will only confuse you. The appropriate reference frame is the one where the platform on the left is fixed, the mechanism holding the belt is fixed, the belt moves a per your arrow from right to left and the car does whatever it is going to do.
If you hold the car in a fixed position in this reference frame, which can be done without the expenditure of any power whatsoever by simply mechanically locking wheel M, you can then generate any arbitrarily large amount of power with wheel G, subject to physical limitations. In this case, and in any case where the car remains fixed or moves at a constant speed, the force applied to wheel G will match that applied to or by wheel M. This results simply from F=MA, where if A = 0 (car not accelerating) then the total F must also equal 0.
What you do with this power is up to you--you can make toast, smelt aluminum or you can apply some of that power to wheel M and move the car. Now once the car is moving there will be a different set of calculations you will need to do to define its steady state--there will be a continuous expenditure of energy at wheel M because there is a force over distance, but you can generate that from wheel G without violating conservation of energy because the energy is coming from the belt. As long as the ratio R is less than one, wheel G will be rotating at a faster rate then wheel M, and since the forces must be equal in a steady state, that means there is always more power available from wheel G than is needed by wheel M. The maximum speed you can attain, which is correlated to the ratio R by those equations you still haven't solved, will be determined by the overall efficiency of the generator/motor combination.