Counterexamples to termination for the direct sum of term rewriting systems

Counterexamples to Termination for the Direct Sum of Term Rewriting Systems

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that the direct sum of two term rewriting systems is not terminating, even if these systems are both terminating. Keyword: Term rewriting system, termination Introduction A term rewriting system R is a set of rewriting rules M → N , where M and N are terms [1, 3, 5]. The di...

On Termination of the Direct Sum of Term-Rewriting Systems

To cite this version: Michaël Rusinowitch. On termination of the direct sum of term rewriting systems. HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouvert...

Termination for the Direct Sum of left-Linear Term Rewriting Systems -Preliminary Draft-

1. I n t r o d u c t i o n An important concern in building algebraic specifications is their hierarchical or modular structure. The same holds for term rewriting systems [1] which can be viewed as implementations of equational algebraic specifications. Specifically, it is of obvious interest to determine which *This paper is an abbreviated version of the IEICE technical report COMP88-30, July ...

Modular Term Rewriting Systems and the Termination

The direct sum of two term rewriting systems (TRSs) [2,8] R, and R, is confluent if R, and R, are confluent [lo], but the direct sum is not necessarily terminating even if R, and R, are terminating [ll]; that is, termination is not a “modular” [6] property for general term rewriting systems. Recently, it was proved [9,5,12,4] that for some restricted classes of systems the direct sum is termina...

Modular Termination of Term Rewriting Systems Revisited