How would you define a set of 'fundamental operations' over an object?
There is no standard notion of "fundamentalness".  It's not clear that what you are looking for is meaningful or makes any sense.  What is "fundamental" is a matter of perspective; I don't see any reason to privilege insert as more fundamental than splice, or vice versa.

So, if you need a concept of "fundamental" for some reason, you'll need to define for yourself what you mean by "fundamental".  If you're going to head that path, I would suggest that you start by asking yourself, "Why do you care?"

Personally, I suspect an XY problem.  I suspect you're asking the wrong question, and you should go back and ask yourself why you want to know and what you will do with the answer -- and that might help you identify a more sensible question or a more pragmatic path to achieving your real goals.