  We introduce a detection algorithm for SAGBI basis in polynomial rings,
analogous to a Gr\"obner basis detection algorithm previously proposed by
Gritzmann and Sturmfels. We also present two accompanying software packages
named SagbiGbDetection for Macaulay2 and Julia. Both packages allow the user to
find one or more term orders for which a set of input polynomials form either
Gr\"obner basis for the ideal they generate or a SAGBI basis for the
subalgebra. Additionally, we investigate the computational complexity of
homogeneous SAGBI detection and apply our implementation to several novel
examples.
