What theory? The theory for the notation does not have anything to say about performance. The "theory" for some hypothetical implemention depends on that hypothetical implementation, which can roughly be divided into logical (query rewrite) & both explicit (indexes) & implicit (other) physical (implementation) aspects. The reality is coarsly guided by those aspects (guaranteed or otherwise) of an actual implementation. Ultimately we must measure for estimated/typical/actual loads & data--performance is chaotic, a small change in circumstances can make a large change in results.
The whole thing is moot though since if you declare constraints & you know the inner & outer joins are the same then the DBMS is extremely likely to also know and if not then extremely likely to do the same amount of work anyway.
Moreover the sort of difference involved is going to be insignificant compared to whatever the actual work getting done is. Entire books await re optimization in general and for DBMSs specifically.
Give arguments to support the following conjectures:
• if n>=10, the time required to initialize a matrix is not very important
• if n<10, the time required to initialize a matrix is not very important
-- Points to Ponder 1.1, Chapter 1 (Introduction), re Rule 1, "Write clearly--don't be too clever", the classic, The Elements of Programming Style by Kernihan & Plauger (1974)