Unfortunately, as noted in your link, the SSSR solution is not unique. Also unfortunate, Daylight (the inventor of SMILES) added SSSR as an optional atom identifier in their SMARTS query specification without realizing this. Because OpenEye doesn't like SSSR, they actually leave out this feature in their implement of SMARTS, breaking from standard.
https://daylight.com/dayhtml/doc/theory/theory.smarts.html
BTW, there is a very clever algorithm for finding SSSR
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2765087/