By means of constructing suitable well quasi-orders of free monoids we prove that all maximal solutions of certain systems of language inequalities are regular. This way we deal with a wide class of systems of inequalities where all constants are languages recognized by finite simple semigroups. In a similar manner we also demonstrate that the largest solution of the inequality XK⊆LX is regular provided the language L is regular. © 2005 Elsevier B.V. All rights reserved.
Kunc, M. (2005). Regular solutions of language inequalities and well quasi-orders. In Theoretical Computer Science (Vol. 348, pp. 277–293). https://doi.org/10.1016/j.tcs.2005.09.018