YES

# parallel critical pair closing system (Shintani and Hirokawa 2022)

Consider the left-linear TRS R:

  W(W(x)) -> W(x)
  B(I(x)) -> W(x)
  W(B(x)) -> B(x)
  F(H(x),y) -> F(H(x),G(y))
  F(x,I(y)) -> F(G(x),I(y))
  G(x) -> x

Let C be the following subset of R:

  W(W(x)) -> W(x)
  B(I(x)) -> W(x)
  G(x) -> x

The TRS R is left-linear and all parallel critical pairs are joinable by C.
Therefore, the confluence of R follows from that of C.

# parallel critical pair closing system (Shintani and Hirokawa 2022)

Consider the left-linear TRS R:

  W(W(x)) -> W(x)
  B(I(x)) -> W(x)
  G(x) -> x

Let C be the following subset of R:

  (empty)

The TRS R is left-linear and all parallel critical pairs are joinable by C.
Therefore, the confluence of R follows from that of C.

# emptiness

The empty TRS is confluent.