Takahito Aoto

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We have developed an automated confluence prover for term rewriting systems (TRSs). This paper presents theoretical and technical ingredients that have been used in our prover. A distinctive feature of our prover is incorporation of several divide–and–conquer criteria such as those for commutative (Toyama, 1988), layer-preserving (Ohlebusch, 1994) and(More)
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our(More)
Rewriting induction (Reddy, 1990) is an automated proof method for inductive theorems of term rewriting systems. Reasoning by the rewriting induction is based on the noetherian induction on some reduction order. Thus, when the given conjecture is not orientable by the reduction order in use, any proof attempts for that conjecture fails; also conjectures(More)
A minimal theorem in a logic L is an L-theorem which is not a nontrivial substitution instance of another L-theorem. Komori (1987) raised the question whether every minimal impli-cational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has been known to be partially positive and generally negative. It(More)
A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (R), which results from R by omitting its sort information, has the property P . It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only(More)