Test cases for Dehornoy's Braid Comparison Algorithm

(I posted this question on the Math StackExchange where it was marked as off-topic)

I am a high school student and as a part of my Extended Essay (required for the completion of the International Baccalaureate Diploma Program (ibo.org)) I am exploring Patrick Dehornoy's braid comparison algorithm in introduced in his A Fast Method for Comparing Braids paper.

I have implemented the algorithm in Python (source available on Github) and I need test cases to check my implementation on. I tried looking for relevant literature using Google searches and JStor, but couldn't find anything.

It would be great if someone could give me some ideas on testing my code, critique the code itself, and/or point me to relevant work in literature.

Thanks a lot.

Abhik