8. Consider two ways to modify the depth-bound meta-interpreter of Figure 14.12:

(a) The bound is on number of instances of base-level atoms that appear in the proof.

Why might this be better or worse than using the depth of the tree?

(b) Allow different base-level atoms to incur different costs on the bound. For example, some atoms could have zero cost, and some atoms could incur a high cost. Give an example of where this might be useful. What conditions on the atom costs would guarantee that, when a positive bound is given, the proof procedure does not go into an infinite loop?