A Characterization of Quasi-Decreasingness

In 2010 Schernhammer and Gramlich showed that quasi-decreasingness of a DCTRS R is equivalent to \mu-termination of its context-sensitive unraveling Ucs® on original terms. While the direction that quasi-decreasingness of R implies \mu-termination of Ucs® on original terms is shown directly; the converse - facilitating the use of context-sensitive termination tools like MU-TERM and VMTL - employs the additional notion of context-sensitive quasi-reductivity of R. In the following, we give a direct proof of the fact that \mu-termination of Ucs® on original terms implies quasi-decreasingness of R. Moreover, we report our experimental findings on DCTRSs from the confluence problems database (Cops), extending the experiments of Schernhammer and Gramlich.