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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)
It is known that in f!;^g-fragment of the natural deduction system of intuitionistic propositional logic NJ balanced formulas have unique-normal proofs. A balanced formula is a formula such that 1. every propositional variable has at most one negative occurrence and 2. every propositional variable has at most one positive occurrence. It will be shown here(More)
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 con-fluence disproving procedure based on these instances. The experiments reveal that(More)
Huet and Lang (1978) presented a framework of automated program transformation based on lambda calculus in which programs are transformed according to a given program transformation template. They introduced a second-order matching algorithm of simply-typed lambda calculus to verify whether the input program matches the template. They also showed how to(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 2(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)