Hi I'm trying to solve this exercise but I can't find any material online, it's not an homework I actually have sort of a solution (it looks incomplete though), but from that I can't really understand much about how to tackle the problem. Anyway we're asked to find a term $\Delta$ such that: $$ \left\{\begin{matrix} \Delta(\lambda x y. x (y(\lambda u.yuy)x)x)=y_1 \\ \Delta(\lambda xy.x(y(\lambda u.yu(\lambda abc.cab))x)x) = y_2 \end{matrix}\right.$$
I looked at a similar exercise where the idea was to define $\Delta$ to be an abstraction of the type $\lambda x. x R_3$ where $R_3$ is the ROTATION operation on Bohm Trees (takes the leftmost child of a tree with k+1 subtrees and makes it the new root).
Could someone please explain me how to solve these type of problems? thanks