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- Takahito Aoto, Yoshihito Toyama
- J. UCS
- 1997

- Takahito Aoto, Junichi Yoshida, Yoshihito Toyama
- RTA
- 2009

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)

- Takahito Aoto, Yoshihito Toyama
- RTA
- 2011

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)

- Takahito Aoto, Toshiyuki Yamada
- RTA
- 2003

- Takahito Aoto
- RTA
- 2010

Decreasing diagrams technique (van Oostrom, 1994) is a technique that can be widely applied to prove confluence of rewrite systems. To directly apply the decreasing diagrams technique to prove confluence of rewrite systems, rule-labelling heuristic has been proposed by van Oostrom (2008). We show how constraints for ensuring confluence of term rewriting… (More)

- Takahito Aoto
- RTA
- 2006

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)

- Takahito Aoto
- Journal of Logic, Language and Information
- 1999

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)

- Takahito Aoto
- FroCos
- 2013

In order to disprove confluence of term rewriting systems, we develop new criteria for ensuring non-joinability of terms based on interpretation and ordering. We present some instances of the criteria which are amenable for automation, and report on an implementation of a confluence disproving procedure based on these instances. The experiments reveal that… (More)

- Takahito Aoto, Toshiyuki Yamada
- RTA
- 2005

- Takahito Aoto
- Journal of Functional and Logic Programming
- 1998

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)