julia> using AbstractAlgebra, Groebner

julia> R, (x1,x2) = polynomial_ring(QQ, ["x1","x2"], internal_ordering=:deglex);

julia> set = [613*x1^2*x2^3 + 1413*x1*x2^2, 428*x1^3*x2 + 529*x1*x2^2]

julia> gb = groebner(set);

julia> isgroebner(gb)
false