Volker Diekert, Yves Metivier, "Partial Commutation and Traces
https://pdfs.semanticscholar.org/d67a/c4c1e5967f7e114f390245...
I think I recall LaBRI being fond of infinite trees for logic programming too. I like trees. I never saw the paper you linked so thanks a lot.
Trace theory seems to have fallen out of academic fashion. I have a feeling it may have a resurgence of interest in coming decades, as it is useful for analysing concurrent systems.