A family of theorems and corollaries are now proven. It will be soon shown that all three categories of software engineering methodologies are complete for static environments. Only cyclical and WaterSluice are complete for dynamic environments while only WaterSluice is complete for non-monotonic environments. The best case performance of the sequential methodology is O(N). The best case performance of the cyclical and the WaterSluice methodology is O(1). The worst case performance of all three categories of methodologies are the same. On average the sequential methodology will find a solution in O(N), the cyclical methodology will find a solution in O(N), 5.1 and the WaterSluice will find a solution in an order-of-magnitude less than N.