YES

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

Consider the left-linear TRS R:

  a() -> c()
  b() -> c()
  f(a(),b()) -> d()
  f(x,c()) -> f(c(),c())
  f(c(),x) -> f(c(),c())
  d() -> f(a(),c())
  d() -> f(c(),b())

Let C be the following subset of R:

  f(x,c()) -> f(c(),c())
  f(c(),x) -> f(c(),c())
  d() -> f(c(),b())

The parallel critical pair system PCPS(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.

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

Consider the left-linear TRS R:

  f(x,c()) -> f(c(),c())
  f(c(),x) -> f(c(),c())
  d() -> f(c(),b())

Let C be the following subset of R:

  (empty)

The parallel critical pair system PCPS(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.