Base and relative pairs. Resolve .. by removing the previous segment.
Do not read these paths from a disk. They are labels.

worked
base: /lab/public
relative: ../draft/note
segments after join: lab, public, .., draft, note
after .. : lab, draft, note
directory of the final segment: draft

activity
base: /lab/public/images
relative: ../../draft/seal
segments after join: lab, public, images, .., .., draft, seal
after the two .. segments: lab, draft, seal
directory of the final segment: draft