  The chase procedure is a fundamental algorithmic tool in database theory with
a variety of applications. A key problem concerning the chase procedure is
all-instances termination: for a given set of tuple-generating dependencies
(TGDs), is it the case that the chase terminates for every input database? In
view of the fact that this problem is undecidable, it is natural to ask whether
known well-behaved classes of TGDs ensure decidability. We consider here the
main paradigms that led to robust TGD-based formalisms, that is, guardedness
and stickiness. Although all-instances termination is well-understood for the
oblivious version of the chase, the more subtle case of the restricted (a.k.a.
the standard) chase is rather unexplored. We show that all-instances restricted
chase termination for guarded and sticky single-head TGDs is decidable.
