  The lower and upper bound of any given algorithm is one of the most crucial
pieces of information needed when evaluating the computational effectiveness
for said algorithm. Here a novel method of Boolean Algebraic Programming for
symbolic manipulation of Machines, Functions, and Inputs is presented which
allows for direct analysis of time complexities and proof of deterministic
methodologies. It is demonstrated through the analysis of a particular problem
which is proven and solved through the application of Boolean algebraic
programming.
