YES

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

Consider the left-linear TRS R:

  +(+(x,y),z) -> +(x,+(y,z))
  +(x,+(y,z)) -> +(+(x,y),z)

Let C be the following subset of R:

  +(x,+(y,z)) -> +(+(x,y),z)

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:

  +(x,+(y,z)) -> +(+(x,y),z)

Let C be the following subset of R:

  (empty)

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

  +(y1,+(y2,+(x1_2,x1_3))) -> +(y1,+(+(y2,x1_2),x1_3))
  +(y1,+(y2,+(x1_2,x1_3))) -> +(+(y1,y2),+(x1_2,x1_3))

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.