YES

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

Consider the left-linear TRS R:

  H(H(x)) -> K(x)
  H(K(x)) -> K(H(x))

Let C be the following subset of R:

  (empty)

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

  H(H(H(x0))) -> H(K(x0))
  H(H(H(x0))) -> K(H(x0))
  H(H(K(x0))) -> H(K(H(x0)))
  H(H(K(x0))) -> K(K(x0))

All pairs in PCP(R) are joinable and PCPS(R,C)/R is terminating.
Therefore, the confluence of R follows from that of C.

# emptiness

The empty TRS is confluent.