The stopping criteria for the main loop in sagbi are: a finite sagbi basis is computed, or the smallest degree of an S-pair exceeds the Limit. In general, the initial terms of generators of a partial computation do not generate the initial algebra up to the degree limit. It is possible that, with a higher degree limit, sagbi generators of lower degree will be added. One can guarantee that all sagbi generators up to a certain degree are found by using a graded term-order such as GRevLex and working with a subring or a polynomial ring (and not a quotient ring).