Inductive learning of recurrence-term languages from positive data

We show that the class of languages generated by (basic) recurrence-terms is inferable in the limit from positive data, and that such learning may be consistent and conservative, though not in general strong monotonic. This class of languages has neither of the properties of finite thickness and finite elasticity usually used to prove inferability from positive data, so our proof method is the explicit construction of a tell-tale function for the class of recurrence-term languages. Recurrence-terms are of interest because they generate many sequences arising from divergent cases of Knuth-Bendix completion.