In this paper we present an interesting gadget based on the chain pair
simplification problem under the discrete Fr\'echet distance (CPS-3F), which
allows the construction of arbitrarily long paths that must be chosen in the
simplification of the two curves. A pseudopolynomial time reduction from set
partition is given as an example. For clarification, CPS-3F was recently shown
to be in \textbf{P}, and the reduction is merely to show how the gadget works