Checking language inclusion between two nondeterministic B ̈ chi au- u tomata A and B is computationally hard (PSPACE-complete). However, several approaches which are efficient in many practical cases have been proposed. We build on one of these, which is known as the Ramsey-based approach. It has recently been shown that the basic Ramsey-based approach can be drastically optimized by using powerful subsumption techniques, which allow one to prune the search-space when looking for counterexamples to inclusion. While previous works only used subsumption based on set inclusion or forward simulation on A and B , we propose the following new techniques: (1) A larger subsumption rela- tion based on a combination of backward and forward simulations on A and B . (2) A method to additionally use forward simulation between A and B . (3) Ab- straction techniques that can speed up the computation and lead to early detection of counterexamples. The new algorithm was implemented and tested on automata derived from real-world model checking benchmarks, and on the Tabakov-Vardi random model, thus showing the usefulness of the proposed techniques.