YES

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

Consider the left-linear TRS R:

  F(x,y) -> c(y)
  G(x) -> x
  f(x) -> g(x)
  g(x) -> c(x)

Let C be the following subset of R:

  (empty)

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

  (empty)

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.