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We introduce a process, dubbed triangulation, turning any rewrite relation into a confluent one. It is more direct than usual completion, in the sense that objects connected by a peak are directly oriented rather than their normal forms. We investigate conditions under which this process preserves desirable properties such as termination.doi:10.4230/lipics.rta.2012.240 dblp:conf/rta/OostromZ12 fatcat:2lfqmtn2mzbsfjoyoyyhivi2rq