regex DoS in postgresql?

I would like to deploy a web application with a Postgresql backend
that allows a user to both add a record containing arbitrary text,
and to search that text column with an arbitrary regular expression.

My question is, is the app subject to a regex denial of service attack?

I would have presumed so but I have been unable produce any problems
when testing using the "evil" regexs described in the Wikipedia
article on the subject: https://en.wikipedia.org/wiki/ReDoS

Is there something in the way Postgresql implements its RE engine
that makes it immune to this attack?

Thanks for any enlightenment...