SLIM is an LMNtal runtime. LMNtal is a programming and modeling language based on hierarchical graph rewriting. SLIM features automata-based LTL model checking that is one of the methods to solve accepting cycle search problems. Parallel search algorithms OWCTY and MAP used by SLIM generate a large number of states for problems having and accepting cycles. Moreover, they have a problem that performance seriously falls for particular problems. We propose a new algorithm that combines MAP and Nested DFS to remove states for problems including accepting cycles. We experimented the algorithm and confirmed improvements both in performance and scalability.