We investigate the existence of the least fixpoint of planning problems in the context of fluent calculus. For that matter, we represent the planning problems as equational logic programs which are restricted to acyclic programs to obtain the least fixpoint of TP . The acyclicity of the program is guaranteed by the existence of a level mapping. To that purpose, we extend the definition of level mapping to satisfy the equivalence class of the equational logic programs. Furthermore, we apply the extended level mapping on the instances of conjunctive planning problems by  and compute the least fixpoint.