  Reaction system is a computing model inspired by the biochemical interaction
taking place within the living cells. Various extended or modified frameworks
motivated by biological, physical, or purely mathematically considerations have
been proposed and received significant amount of attention, notably in the
recent years. This study, however, takes after particular early works that
concentrated on the mathematical nature of minimal reaction systems in the
context-free basic framework and motivated by a recent result on the
sufficiency of strictly minimal reaction systems to simulate every reaction
system. This paper focuses on the largest reaction system rank attainable by
strictly minimal reaction systems, where the rank pertains to the minimum size
of a functionally equivalent reaction system. Precisely, we provide a very
detailed study for specific strictly minimal reaction system induced by
permutations, up to the quaternary alphabet. Along the way, we obtain a general
result about reaction system rank for Cartesian product of functions specified
by reaction systems.
