What's the (Big O) computational complexity of a PostgreSQL recursive common table expression?

For example, taking this StackOverflow #44620695 question, recursive path aggregation and CTE query for top-down tree postgres as an example, which uses a recursive CTE to traverse a tree structure to determine the paths from a starting node.

The screenshot above shows the the input data, the recursive CTE result, and a visualization of the source data.

Recursive CTE are iterative over the preceding result -- right? (as suggested in the accepted answer here) -- so would the time complexity be something like O(log n)?