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This paper represents system models as algebraic entities and formulates model transformation activities as algebraic operations. We call this modeling framework ldquoalgebra of systemsrdquo (AoS). To show that AoS can automate complex model reasoning tasks in system design projects, we implemented the abstract algebraic specification as an executable metalanguage named object-process network, which serves as a tool for automatic model transformation, enumeration, and evaluation. A case study of the Apollo lunar landing mission design is developed using this algebraic modeling approach.