Abstract
Fay has described in [2,3] a complete T-unification for equational theories T which possess a complete set of reductions as defined by Knuth & Bendix [12]. This algorithm relies essentially on using the narrowing process defined by Lankford [13]. In this paper, we first study the relations between narrowing and unification and we give a new version of Fay's algorithm. We then show how to eliminate many redundancies in this algorithm and give a sufficient condition for the termination of the algorithm. In a last part, we show how to extend the previous results to various kinds of canonical term rewriting systems.
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Hullot, JM. (1980). Canonical forms and unification. In: Bibel, W., Kowalski, R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10009-1_25
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DOI: https://doi.org/10.1007/3-540-10009-1_25
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