YES

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

Consider the left-linear TRS R:

  F(c(x)) -> G(x)
  G(x) -> F(x)
  c(x) -> x

Let C be the following subset of R:

  (empty)

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

  F(c(y0)) -> F(y0)
  F(c(y0)) -> G(y0)

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.