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The widespread automation of e-business processes has made workflow analysis and design an integral part of information management. Graph-based workflow models enables depicting complex processes in a fairly compact form. This free form, on the other hand, can yield models that may fail depending on the judgment of the modeler and create modeling situations that cannot be executed or will behave in a manner not expected by the modeler. Further, cycles in workflow models needed for purposes of rework and information feedback increase the complexity of workflow analysis. This paper presents a novel method of partitioning a cyclic workflow process, represented in a directed graph, into a set of acyclic subgraphs. This allows a cyclic workflow model to be analyzed further with several smaller subflows, which are all acyclic. As a convincing example, we present two-phased verification of structural conflicts in workflow models for those incurred from the inappropriate composition of partitioned flows and the others within each acyclic subgraph, which is much easier to comprehend and verify individually than the whole workflow model, in general.