The language of all borderless words
The borderless words are also known as unbordered or bifix-free ("A note on bifix-free sequences", PT Nielsen, in a paper as early as 1973).

The language of unbordered words is not even context-free, see the paper "Inverse star, borders, and palstars" by Ramparsad etal, in TCS with a preprint on ArXiv. The technique to obtain this result is Ogden's Lemma, an extension of classical pumping, and discussed elsewhere on this forum.