In order to support run-time computation outsourcing to save energy, a certain amount of overhead has to be incurred to facilitate appropriate communication. As computation outsourcing is a methodology for saving energy on mobile devices, the amount of overhead incurred must be kept to a minimum. In this work, we support our compile-time methodology to facilitate the outsourcing of intensive computation with a run-time monitoring system that consumes an extremely low amount of energy (near-Zero). This near-Zero overhead resulted from analyzing the code at compile-time rather than run-time execution and profiling. The compile-time strategy utilized in our work analyzes the code at multiple levels of abstraction (High, Medium, and Low). The result of the analysis, which takes advantage of a real-time systems technique that calculates the maximum number of loop iterations, hence giving us a worst-case execution time for each loop within the benchmark application, allows for a fine-grain analysis of our benchmark. Resulting from analyzing the code, a client/server version of the applications is produced. As a result of producing this client/server version, certain run-time support has to take place on both the machine executing the client (the mobile device) as the machine executing the server. Our experimental results as performed on a Sharp Zaurus, utilizing Wi-Fi as a means of communication, showed tremendous energy saving while incurring a near-Zero run-time overhead.