Henselian ring which is not complete

Question

Henselian ring is defined as a local ring which has the property that Hensel's lemma holds.

I understand that completeness is sufficient condition to be Henselian, but is not necessary condition.

So, there should be example of a local ring which is Henselian, but not complete.

I would like to know such examples.

Thank you in advance.

Answer 1

The henselization of the $p$-adic integers is an example, and also $k[x^{1/2}, x^{1/4}, x^{1/8},\ldots]/(x)$.