A function where step-size adaptation is decisive?

[nikohansen]

Step-size adaptation has the following benefits:

• allows to recover from a (initially) far too small sample variance

• increases the convergence speed (like on the sphere function)

• allow that the number of evaluations scales linearly with increasing dimension (like on the sphere function)

Now, I am looking for an example where step-size adaptation decisively helps but that does not fall in any of the above categories. That is, a function where CMA-ES with step-size adaptation works but without step-size adaptation fails even when the initial variance is chosen large enough.