The reachability and joinability problems for right-ground term-rewriting systems
Journal of Information Processing
Handbook of theoretical computer science (vol. B)
Syntacticness, cycle-syntacticness, and shallow theories
Information and Computation
Lazy narrowing: strong completeness and eager variable elimination
TAPSOFT '95 Selected papers from the 6th international joint conference on Theory and practice of software development
A deterministic lazy narrowing calculus
Journal of Symbolic Computation
Unification in Extension of Shallow Equational Theories
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
Basic Paramodulation and Decidable Theories
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
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The unification problem for term rewriting systems(TRSs) is the problem of deciding, for a given TRS R and two terms M and N, whether there exists a substitution θ such that Mθ and Nθ are congruent modulo R (i.e., Mθ ↔R* Nθ). In this paper, the unification problem for confluent right-ground TRSs is shown to be decidable. To show this, the notion of minimal terms is introduced and a new unification algorithm of obtaining a substitution whose range is in minimal terms is proposed. Our result extends the decidability of unification for canonical (i.e., confluent and terminating) right-ground TRSs given by Hullot (1980) in the sense that the termination condition can be omitted. It is also exemplified that Hullot's narrowing technique does not work in this case. Our result is compared with the undecidability of the word (and also unification) problem for terminating right-ground TRSs.