## Section: New Results

### On the Length of Medial-Switch-Mix Derivations

Participant : Lutz Straßburger.

Switch and medial are two inference rules that play a central role in many deep inference proof systems. In specific proof systems, the mix rule may also be present. In a joint work with Paola Bruscoli (University of Bath) we show that the maximal length of a derivation using only the inference rules for switch, medial, and mix, modulo associativity and commutativity of the two binary connectives involved, is quadratic in the size of the formula at the conclusion of the derivation. This shows, at the same time, the termination of the rewrite system. This result has been presented at the International Workshop on Logic, Language, Information, and Computation 2017 [20].