The Conley Decomposition Theorem [1] is one of the most fundamental theorems in the theory of dynamical systems. Charles Conley introduced a very weak form of recurrence for flows, which he called ”chain recurrence”. He then proved the existence of what he termed as ”complete Lyapunov function”, a real-valued function strictly decreasing everywhere except on components of the chain-recurrent set, where it is constant. A similar theorem holds true for iterations of continuous functions [2], and of closed relations [3]. D. Norton calls Conley’s theorem ”The Fundamental Theorem of the Dynamical Systems”.