Punctuation with "and thus" in the middle of a sentence

I was wondering if I have to place a comma before and after "and thus". Usually, this is followed by a comma, but in this sentence, I think one comma before it is enough. Right?

"accepted theories can provide satisfactory results, and thus, experiments can be avoided."

This sentence has two independent clauses. They are connected by "and" with a comma before it. The "and" and the comma are correct. However, adding a comma after "thus" is not correct because it is an adverb; the comma after it is not necessary.

The sentence is fine this way:

"Accepted theories can provide satisfactory results, and thus experiments can be avoided."

If "thus" is used as a conjunctive adverb (without "and"), a semi-colon and a comma are necessary. This version of your sentence is also correct:

"Accepted theories can provide satisfactory results; thus, experiments can be avoided."

Both of these sentences are clearer than your sentence that has the comma after "thus."