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Some [Formula: see text]-equivalence preserving rewriting rules for such terms are introduced. A characterization of terms that are only [Formula: see text]-equivalent to themselves is studied for binary signatures. Graphs associated to the equivalence classes of [Formula: see text]-equivalent terms are studied with respect to graph distance. Finally, the preservation of [Formula: see text]-equivalence under the term self-shuffle operator is studied. <\/jats:p>","DOI":"10.1142\/s0129054120500306","type":"journal-article","created":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T10:16:36Z","timestamp":1597313796000},"page":"621-638","source":"Crossref","is-referenced-by-count":2,"title":["A New Study of Parikh Matrices Restricted to Terms"],"prefix":"10.1142","volume":"31","author":[{"given":"Zi Jing","family":"Chern","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8726-5850","authenticated-orcid":false,"given":"K. 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