[hairtuq]

This will not yield a minimal set; in a cycle, it is only necessary to remove at least one word. The problem is thus to delete the minimum number of vertices to remove all cycles. This is the NP-hard Feedback Vertex Set problem. Here's a paper that solves it for a dictionary (there is some more): https://arxiv.org/abs/0911.5703

[titanix2]

I checked the comments to check if this paper was mentioned anywhere. Good recommendation.

[fginionio]

Looks like you found our answer! Someone's already done the hard work.

[zuminator]

This is not necessarily the answer. It's an upper-bound for the answer.