I have already studied several papers related to composition-diamond Lemma completely and now I am familiar with theoretical tools. For instance I realized the concept of associative Lyndon-Shirshov words, non-associative lyndon-shirshov words and their properties plus necessary lemmas and theorems.
Now I would like to utilize those theoretical tools for a small example. May you please help me to find an effective example of a free Lie algebras to construct a Groebner-Shirshov basis?