For 2:1
X = 1m (distance the vehicle body moved relative to ground).
Y = 2m (distance the treadmill surface moved relative to ground).
No. You pulled that out of your arse, and it is incorrect.
With a 2:1 gearing, i.e. wheels of the same size, belt with driven side pulley half the size of the driver side pulley, the vehicle will travel at exactly the same speed right with respect to ground, as the treadmill surface moves left with respect to ground.
In other words, for 2:1 gearing, using a belt (treadmill side pulley half the diameter of the driver side pulley),
x = 1m (distance the vehicle body moved right relative to ground).
y = 1m (distance the treadmill surface moved left relative to ground)
This is because the driven wheel turned twice the amount the driver wheel turned.
In other words, the contact point on the driver wheel (between driver wheel and ground) rotated a distance of 1m, but the contact point on the driven wheel (between driven wheel and treadmill surface) rotated a distance of 2m. This is necessary for the distance between the two wheels to stay constant.
Remember, while the treadmill surface moves left by 1m, the driven wheel moves right by 1m, and thus it must rotate enough for 2m of travel.