Аннотация:In 1993 Mati Pentus proved a criterion of conjoinability for the Lambek calculus and multiplicative cyclic linear logic. In 2011 Alexey Sorokin showed that any pair of conjoinable types in the Lambek calculus has the join type of quadratic length with respect to the length of the types in the pair. We prove that the lower bound on the length of joins in the Lambek calculus and multiplicative linear logic is also quadratic.