Here you can download a program written in Python 2 which serves to find all the one-element Rees co-extensions of a given finite, negative, totally ordered monoid. As a byproduct, all such monoids up to a given finite size can be determined.
The details on the algorithm are in the following papers:
- M. Petrík and T. Vetterlein. Rees coextensions of finite tomonoids and free pomonoids. Semigroup Forum 99 (2019) 345-367. DOI: 10.1007/s00233-018-9972-z. [PDF]
- M. Petrík and T. Vetterlein. Rees coextensions of finite, negative tomonoids. Journal of Logic and Computation 27 (2017) 337-356. DOI: 10.1093/logcom/exv047. [PDF]
The code has been recently completely rewritten and published as a Python 3 library on PyPI. See:
