YES

# Compositional critical pair system (Shintani and Hirokawa 2022).

Consider the left-linear TRS R:

  s(p(x)) -> x
  p(s(x)) -> x

Let C be the following subset of R:

  (empty)

The critical pair system CPS(R,C) is:

  p(s(p(x0))) -> p(x0)
  s(p(s(x0))) -> s(x0)

The TRS R is locally confluent and CPS(R,C)/R is terminating.
Therefore, the confluence of R follows from that of C.

# Emptiness.

The empty TRS is confluent.