Two new open problems about relationships of funcoids and reloids

In the past I overlooked the following two open problems considering them obvious. When I tried to write proofs of these statements down I noticed these are not trivial. So I added them to my list of open problems.

Question (\mathsf{RLD})_{\mathrm{out}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B}) = \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B} for every filter objects \mathcal{A}, \mathcal{B}?

Conjecture (\mathsf{RLD})_{\mathrm{out}} {(=)}|_{\mathcal{A}} = {(=)}|_{\mathcal{A}} for every filter object \mathcal{A}.

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