YES

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

Consider the left-linear TRS R:

  a(a(x)) -> a(b(a(x)))
  b(a(b(x))) -> a(c(a(x)))

Let C be the following subset of R:

  (empty)

The parallel critical pair system PCPS(R,C) is:

  a(a(a(x1_1))) -> a(a(b(a(x1_1))))
  a(a(a(x1_1))) -> a(b(a(a(x1_1))))
  b(a(b(a(b(x2_1))))) -> b(a(a(c(a(x2_1)))))
  b(a(b(a(b(x2_1))))) -> a(c(a(a(b(x2_1)))))

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.