Partial pullback complement rewriting

We then propose a new graph rewriting technique, called the partial pullback complement rewriting, that uses pullback complements in a partial morphism category. We finally compare this with the double-pullback, single pushout, double-pushout and sesqui-pushout techniques, proving that in certain categories and under certain conditions, the partial pullback complement rewriting, implies and/or is implied by the above mentioned rewritings. Some illustrative examples are also given.