That said: it's an implementation which doesn't behave like normal regexps (it's a left-shortest match first instead of the common left-longest) and it's a back-tracker. Because this implementation doesn't allow much choice, expensive examples will look contrived, but extending this implementation with character sets, groups and choices (i.e. a|b) will make its exponential nature felt very quickly.
> extending this implementation
The exercises at the end of the chapter ask the student to extension the implementation along these lines. Including support for utf8.
> exponential nature
Both the essay and the book highlight this issue. The latter comments that some commercial greps (at the time) also had exponential behavior. https://archive.org/details/practiceofprogra0000kern/page/22...
(I didn't choose exactly the same grep sublanguage to implement -- it was something like supporting the most basic escaping instead of ^ and $.)