Synthesizing ranking functions is a typical technique for proving loop termination. In this work, we propose an approach to handle the backward, or the reverse, problem. That is, one constructs loops such that a given linear function is a ranking function for these loops. To achieve this, we firstly demonstrate by experiments the necessity to introduce parameters to increase the success ratio. We then formulate this problem as a proper existential quantifier elimination (or parametric system solving) problem, and propose two efficient methods to handle it. We have implemented our methods and demonstrated their effectiveness by extensive experiments.