Edit minimum distance replace cost

Course Q&A Natural Language Processing NLP with Probabilistic Models
1

I have a question on the replace cost of Minimum edit distance, in NLP course 2, it says the replace cost is 2, which needs 1 delete and 1 insert. My understanding is replace cost should be 1, many materials on the internet shows it’s 1.

for example to change ‘play’ to ‘stay’, by intuition, we need to replace ‘p’ to ‘s’, ‘l’ t o ‘t’, two replacement as simple as that, cost should be 2, why need a deletion and insert for each replacement?

2

It’s the definition that they use on the course, for the matter of making it simpler that emphasizes insertions/deletions.