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The GYO algorithm then proceeds as follows:
* Find an ear ''e'' in ''H''.
* Remove ''e'' and remove all vertices of ''H'' that are only in ''e''.
If the algorithm successfully eliminates all vertices, then the hypergraph is α-acylic. Otherwise, if the algorithm gets to a non-emtpy hypergraph that has no ears, then the original hypergraph was not α-acyclic:
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