def METHOD_NAME():
    S = SymmetricGroup(4)
    S.schreier_sims()
    base = S.base
    strong_gens = S.strong_gens
    strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
    result = _orbits_transversals_from_bsgs(base, strong_gens_distr)
    orbits = result[0]
    transversals = result[1]
    base_len = len(base)
    for i in range(base_len):
        for el in orbits[i]:
            assert transversals[i][el](base[i]) == el
            for j in range(i):
                assert transversals[i][el](base[j]) == base[j]
    order = 1
    for i in range(base_len):
        order *= len(orbits[i])
    assert S.order() == order