On computing the factor-free basis of a regular language
A language $L$ is infix-free if
$$ L \cap (\Sigma^+L\Sigma^* \cup \Sigma^*L\Sigma^+) = \emptyset. $$
(This deep observation, which I made independently, appears in reference [1] to the paper you cite.) This gives a simple algorithm for deciding whether a regular language $L$ (given as a DFA, NFA, or regular expression) is infix-free.

Similarly, the basis of $L$ is
$$ L \setminus (\Sigma^+L\Sigma^* \cup \Sigma^*L\Sigma^+). $$
This gives a simple algorithm for computing the basis of a regular language (as a DFA, NFA, or regular expression).