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I'm trying to learn how a depth-first search STRIPS algorithm knows how to detect interacting subgoals.

Here is an instance that confuses me. This is a powerpoint slide given to me by my professor, but I'm not sure how he's reaching the conclusion of an interacting subgoal. The problem at hand is the very traditional A,B,C block scheme so I believe most people will be familiar with it.

I understand the common sense aspect of how stacking block A on block C before stacking block C on block B would be counterproductive, but what would be the best way for a computer to discover this negative goal interaction?