Is there a language for which any string (that works) can be shown to not be pumped using the Pumping Lemma?
I'd say the language $L = $ { $0^n1^n | n &gt; 0$ } fits the bill for the Pumping Lemma for Regular Languages.  Any substring to be pumped would consist either of all the same symbol, in which case pumping up produces a string with an unequal number of $0$'s and $1$'s, or it contains instances of both symbols, in which case pumping up produces a string with a $1$ followed by a $0$; in neither case is the pumped-up string in $L$.