  We propose a novel algorithm to decide the language inclusion between
(nondeterministic) B\"uchi automata, a PSPACE-complete problem. Our approach,
like others before, leverage a notion of quasiorder to prune the search for a
counterexample by discarding candidates which are subsumed by others for the
quasiorder. Discarded candidates are guaranteed to not compromise the
completeness of the algorithm. The novelty of our work lies in the quasiorder
used to discard candidates. We introduce FORQs (family of right quasiorders)
that we obtain by adapting the notion of family of right congruences put
forward by Maler and Staiger in 1993. We define a FORQ-based inclusion
algorithm which we prove correct and instantiate it for a specific FORQ, called
the structural FORQ, induced by the B\"uchi automaton to the right of the
inclusion sign. The resulting implementation, called FORKLIFT, scales up better
than the state-of-the-art on a variety of benchmarks including benchmarks from
program verification and theorem proving for word combinatorics.
