I think you’ve arrived at the structure that WP doesn’t quite support.
Let’s start with following premises:
- Taxonomies exist for grouping posts.
- Hierarchical taxonomies can have multiple level of grouping (with larger groups encompassing smaller groups).
But what you had drafted is something else — taxonomy grouping another taxonomy. Simply put that’s not in the plan. 🙂
It’s a little hard to advice without seeing actual data, but my guess would be that if Program/Exercise are taxonomies and need to have nested relationship then they likely just need to be one hierarchical taxonomy.
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