In the following theorems the waterfall methodology is mapped to a breadth-first search algorithm, the spiral methodology to a depth-first search algorithm, and the WaterSluice methodology to a best-first search algorithm.
All three methodologies are complete for a static search space. The problem comes in a dynamic search space. The waterfall methodology will miss a solution. Both the spiral methodology and the WaterSluice methodology will find a solution in a dynamic search space. The WaterSluice methodology will find a solution in less than or equal time to the other two methodologies.