Proofs of the convergence of the rewriting system for the weaving of aspects in the AO - PFA language ∗

AO-PFA is an aspect oriented feature modelling language. This report discusses several theoretical issues regarding the weaving process of AO-PFA. The weaving of aspects is to extract subterms from product family terms in the base specification, and then to replace the extracted subterm (selected join points) by another term (advice). The problem of extracting a subterm from another term is related to what is known as the word problem, which is undecidable in general. In this technical report, we give the detailed proofs related to the termination and confluence (i.e., convergence) of the rewriting system for weaving aspects in AO-PFA. We show that the word problem associated to AO-PFA is decidable. We also prove the unambiguousness of the weaving results by putting some restrictions on the kind of the pointcut of the aspects in AO-PFA.