In this question $R$ is a commutative noetherian local ring with unity.

One can construct examples of rings $R$ and *zerodivisors* $z$ such that $\dim R/(z)=\dim R-1$, e.g., $S\colon=k[a,b,c],\ \mathfrak{m}\colon=(a,b,c),\ R\colon=S_\mathfrak{m}/(a^2,ab)S_\mathfrak{m},\ z\colon=b^2$.

One can also construct examples of rings $R$ and *zerodivisors* $z$ such that $\mathrm{depth}\ R/(z)=\mathrm{depth}\ R-1$, e.g., $S\colon=k[a,b,c],\ \mathfrak{m}\colon=(a,b,c),\ R\colon=S_\mathfrak{m}/(a^2)S_\mathfrak{m},\ z\colon=ab.$

What is an example of a zerodivisor that will reduce *both* the dimension *and* the depth by $1$, simultaneously? Is that possible?