If the CTE is using recursion then its uses a spool operator therefore tempdb is used....therefore not much performance benefit vs just creating a temp table
How exactly would you replace a recursive CTE with a temp table?
If the CTE is non recursive then then the main qry is repeated and performance is that of using a cursor..the main anchor query is repeated therefor performance is no good!
If the CTE is non-recursive, it doesn't have an anchor query (anchor query is only for recursive CTEs), nor is there any query to repeat, I'm not sure what you're getting at here.
A non-recursive CTE is just a named subquery or temporary view, whichever you prefer to imagine it as, and performs as such.
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