In this paper we investigate the possibility of developing a (semi-)automatic rewriting tool for manipulating and reasoning about combinators for Intuitionistic Linear Logic. In particular, we develop a canonical (i.e. confluent and terminating) term rewriting system associated to a theory of categorical combinators for (rudimentary) Linear Logic. In order to do that, we make use of the Knuth-Bendix completion algorithm [3] to transform the equational theory for the combinators into an equivalent...