You mean that you wish to simplify the problem so that you can solve it -- well that's okay but not much of a teaser.
Sorry what I meant to say was that sometimes puzzles have hidden difficulties which unless pointed out may invalidate the puzzle.
Here the hidden question is whether the top cylinder is always in contact as it rolls, if not then it is not continuously accellerated and also bounces.
To start the ball you have to assume a surface depression this accellerates the ball upwards and sideways and therefore it will leave the surface as the depression reaches maximum rebound, Second point is that rolling assumes a coefficient of friction whioch unless stated does not tell you if on contact slippage occurs.
You see I am not attacking here just for the sake of it this puzzle has a wealth of hidden complexity. If you are not interested ignore but others may wish to think about it.