def METHOD_NAME():
    S = SymmetricGroup(10)
    base, strong_gens = S.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(S, base, new_gens) is True
    A = AlternatingGroup(7)
    base, strong_gens = A.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(A, base, new_gens) is True
    D = DihedralGroup(2)
    base, strong_gens = D.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(D, base, new_gens) is True
    D = DihedralGroup(2)
    base, strong_gens = D.schreier_sims_incremental()
    strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
    _, transversals = _orbits_transversals_from_bsgs(base, strong_gens_distr)
    new_gens = _remove_gens(base, strong_gens, transversals, strong_gens_distr)
    assert _verify_bsgs(D, base, new_gens) is True