Abstract: We introduce a novel method for encoding cost optimal delete-free STRIPS Planning as SAT. Our method is based on representing any relaxed plan as a partial function from the set of propositions to the set of actions. This function can map any proposition to a unique action that adds the proposition during execution of the relaxed plan. We show that a relaxed plan can be produced by maintaining acyclicity in the graph of all causal relations among propositions, represented by the mentioned partial function. We also show that by efficient encoding of action cost propagation and enforcing a series of upper bounds on the total costs of the output plan, an optimal plan can effectively be produced for a given delete-free STRIPS problem. Our empirical results indicate that this method is quite competitive with the state-of-the-art, demonstrating a better coverage compared to that of competing methods on conventional STRIPS planning problems.