  This note illustrates theoretical worst-case scenarios for groundness
analyses obtained through abstract interpretation over the abstract domains of
definite (Def) and positive (Pos) Boolean functions. For Def, an example is
given for which any Def-based abstract interpretation for groundness analysis
follows a chain which is exponential in the number of argument positions as
well as in the number of clauses but sub-exponential in the size of the
program. For Pos, we strengthen a previous result by illustrating an example
for which any Pos-based abstract interpretation for groundness analysis follows
a chain which is exponential in the size of the program. It remains an open
problem to determine if the worst case for Def is really as bad as that for
Pos.
