There are two possible values for Strategy: Top and Engine.
There are two implementations to subduct the $S$-pairs in the function sagbi. Both implementations follow the same procedure, but are coded in different parts of Macaulay2. Subduction using the Strategy Top (default) is generally faster for smaller inputs. Subduction using the Engine implementation can be faster for larger subalgebra bases.
When using the Top Strategy, the status of the computation using sagbi can be displayed using the PrintLevel option.
The object SubductionMethod is a symbol.