A decision algorithm for reversible pairs of polygons

A given pair of convex polygons α and β is said to be reversible if α has a dissection into a finite number of pieces which can be rearranged to form β under some conditions. In this paper, we give an algorithm to decide whether or not a given pair of polygons α and β is reversible. Furthermore, a method of how to dissect α to make β, when they are reversible, is also given.