  In 2010 Schernhammer and Gramlich showed that quasi-decreasingness of a DCTRS
R is equivalent to \mu-termination of its context-sensitive unraveling Ucs(R)
on original terms. While the direction that quasi-decreasingness of R implies
\mu-termination of Ucs(R) 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(R) 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.
