Recently it was shown that PLS is not contained in PPADS (ECCC report TR22-058). We show that this separation already implies that PLS is not contained in PPP. These separations are shown for the decision tree model of TFNP and imply similar separations in the type-2, relativized model.

Important note. This manuscript is based on an early preprint of report TR22-058, which did not contain the result that PLS is not contained in PPP. Our work is superseded by the revised version of the report of 10 June 2022 which, independently, contains this result. The manuscript has not been edited to reflect this, and in particular references to the report are to the early version.