The function sagbi computes a sagbi basis by subducting S-pairs. Any resulting non-zero polynomials are added to the list of sagbi generators. However if ReduceNewGenerators is set to true (by default) then the new generators are reduced using gaussian elimination against the other new generators. This process is quick (as fast as computing a groebner basis for a linear ideal) and ensures that duplicate generators are not added to the list of sagbi generators.
The object ReduceNewGenerators is a symbol.