@testset "1712.07167 Examples" begin

    @testset "SL(3,Z)" begin
        N = 3
        G = MatrixAlgebra(zz, N)
        S = PropertyT.generating_set(G)
        autS = WreathProduct(SymmetricGroup(2), SymmetricGroup(N))

        NAME = "SL($N,Z)_orbit"

        rm(NAME, recursive=true, force=true)
        sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(1000, accel=20);
        upper_bound=0.27, force_compute=false)

        @info sett

        λ = PropertyT.spectral_gap(sett)
        @test λ < 0.0
        @test PropertyT.interpret_results(sett, λ) == false

        # second run just checks the solution due to force_compute=false above
        @test λ == PropertyT.spectral_gap(sett)
        @test PropertyT.check_property_T(sett) == false

        sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(4000, accel=20);
        upper_bound=0.27, force_compute=true)

        @info sett

        λ = PropertyT.spectral_gap(sett)
        @test λ > 0.269999
        @test PropertyT.interpret_results(sett, λ) == true

        # this should be very fast due to warmstarting:
        @test λ ≈ PropertyT.spectral_gap(sett) atol=1e-5
        @test PropertyT.check_property_T(sett) == true

        ##########
        # Symmetrizing by SymmetricGroup(3):

        sett = PropertyT.Settings(NAME, G, S, SymmetricGroup(N), with_SCS(4000, accel=20, warm_start=false);
        upper_bound=0.27, force_compute=true)

        @info sett

        λ = PropertyT.spectral_gap(sett)
        @test λ > 0.269999
        @test PropertyT.interpret_results(sett, λ) == true
    end

    @testset "SL(4,Z)" begin
        N = 4
        G = MatrixAlgebra(zz, N)
        S = PropertyT.generating_set(G)
        autS = WreathProduct(SymmetricGroup(2), SymmetricGroup(N))

        NAME = "SL($N,Z)_orbit"

        rm(NAME, recursive=true, force=true)
        sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(2000, accel=20);
        upper_bound=1.3, force_compute=false)

        @info sett

        λ = PropertyT.spectral_gap(sett)
        @test λ < 0.0
        @test PropertyT.interpret_results(sett, λ) == false

        # second run just checks the solution due to force_compute=false above
        @test λ == PropertyT.spectral_gap(sett)
        @test PropertyT.check_property_T(sett) == false

        sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(15000, accel=20, warm_start=true);
        upper_bound=1.3, force_compute=true)

        @info sett

        λ = PropertyT.spectral_gap(sett)
        @test λ > 1.2999
        @test PropertyT.interpret_results(sett, λ) == true

        # this should be very fast due to warmstarting:
        @test λ ≈ PropertyT.spectral_gap(sett) atol=1e-5
        @test PropertyT.check_property_T(sett) == true
    end

    @testset "SAut(F₃)" begin
        N = 3
        G = SAut(FreeGroup(N))
        S = PropertyT.generating_set(G)
        autS = WreathProduct(SymmetricGroup(2), SymmetricGroup(N))

        NAME = "SAut(F$N)_orbit"

        rm(NAME, recursive=true, force=true)

        sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(1000);
        upper_bound=0.15)

        @info sett

        @test PropertyT.check_property_T(sett) == false
    end
end