YES

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

Consider the left-linear TRS R:

  b(w(x)) -> w(w(w(b(x))))
  w(b(x)) -> b(x)
  b(b(x)) -> w(w(w(w(x))))
  w(w(x)) -> w(x)

Let C be the following subset of R:

  (empty)

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

  w(b(w(x0))) -> w(w(w(w(b(x0)))))
  w(b(w(x0))) -> b(w(x0))
  b(b(w(x0))) -> b(w(w(w(b(x0)))))
  b(b(w(x0))) -> w(w(w(w(w(x0)))))
  b(w(b(x0))) -> b(b(x0))
  b(w(b(x0))) -> w(w(w(b(b(x0)))))
  w(w(b(x0))) -> w(b(x0))
  w(b(b(x0))) -> w(w(w(w(w(x0)))))
  w(b(b(x0))) -> b(b(x0))
  b(b(b(x0))) -> b(w(w(w(w(x0)))))
  b(b(b(x0))) -> w(w(w(w(b(x0)))))
  b(w(w(x0))) -> b(w(x0))
  b(w(w(x0))) -> w(w(w(b(w(x0)))))
  w(w(w(x0))) -> w(w(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.