YES

(format LCTRS)
(fun f 2 :sort (Unit Unit Unit))

(rule (f (f x_0 y_1) z_2) (f x_0 (f y_1 z_2)) :vars ((x_0 Unit) (y_1 Unit) (z_2 Unit)))
(rule (f x_3 y_4) (f y_4 x_3) :vars ((x_3 Unit) (y_4 Unit)))

Confluent by Strongly Closedness with proof:
* CriticalPair
  Left rule: (f (f x_0_L y_1_L) z_2_L) -> (f x_0_L (f y_1_L z_2_L))
  Right rule: (f (f x_0_R y_1_R) z_2_R) -> (f x_0_R (f y_1_R z_2_R))
  Critical pair: (f (f x_0_L (f y_1_L y_1_R)) z_2_R) ≈ (f (f x_0_L y_1_L) (f y_1_R z_2_R))
 which reaches the trivial constrained equation
  (≈ (f (f x_0_L (f y_1_L y_1_R)) z_2_R) (f (f x_0_L y_1_L) (f y_1_R z_2_R))) []
	-> (≈ (f x_0_L (f (f y_1_L y_1_R) z_2_R)) (f (f x_0_L y_1_L) (f y_1_R z_2_R))) []
	-> (≈ (f x_0_L (f y_1_L (f y_1_R z_2_R))) (f (f x_0_L y_1_L) (f y_1_R z_2_R))) []
	-> (≈ (f x_0_L (f y_1_L (f y_1_R z_2_R))) (f x_0_L (f y_1_L (f y_1_R z_2_R)))) []
 and the trivial constrained equation
  (≈ (f (f x_0_L (f y_1_L y_1_R)) z_2_R) (f (f x_0_L y_1_L) (f y_1_R z_2_R))) []
	-> (≈ (f (f x_0_L (f y_1_L y_1_R)) z_2_R) (f (f y_1_R z_2_R) (f x_0_L y_1_L))) []
	-> (≈ (f (f x_0_L (f y_1_L y_1_R)) z_2_R) (f y_1_R (f z_2_R (f x_0_L y_1_L)))) []
	-> (≈ (f (f x_0_L (f y_1_L y_1_R)) z_2_R) (f (f z_2_R (f x_0_L y_1_L)) y_1_R)) []
	-> (≈ (f (f x_0_L (f y_1_L y_1_R)) z_2_R) (f z_2_R (f (f x_0_L y_1_L) y_1_R))) []
	-> (≈ (f (f x_0_L (f y_1_L y_1_R)) z_2_R) (f z_2_R (f x_0_L (f y_1_L y_1_R)))) []
	-> (≈ (f z_2_R (f x_0_L (f y_1_L y_1_R))) (f z_2_R (f x_0_L (f y_1_L y_1_R)))) []
* CriticalPair
  Left rule: (f x_3_L y_4_L) -> (f y_4_L x_3_L)
  Right rule: (f (f x_0_R y_1_R) z_2_R) -> (f x_0_R (f y_1_R z_2_R))
  Critical pair: (f z_2_R (f x_0_R y_1_R)) ≈ (f x_0_R (f y_1_R z_2_R))
 which reaches the trivial constrained equation
  (≈ (f z_2_R (f x_0_R y_1_R)) (f x_0_R (f y_1_R z_2_R))) []
	-> (≈ (f (f x_0_R y_1_R) z_2_R) (f x_0_R (f y_1_R z_2_R))) []
	-> (≈ (f x_0_R (f y_1_R z_2_R)) (f x_0_R (f y_1_R z_2_R))) []
 and the trivial constrained equation
  (≈ (f z_2_R (f x_0_R y_1_R)) (f x_0_R (f y_1_R z_2_R))) []
	-> (≈ (f z_2_R (f x_0_R y_1_R)) (f (f y_1_R z_2_R) x_0_R)) []
	-> (≈ (f z_2_R (f x_0_R y_1_R)) (f (f z_2_R y_1_R) x_0_R)) []
	-> (≈ (f z_2_R (f x_0_R y_1_R)) (f z_2_R (f y_1_R x_0_R))) []
	-> (≈ (f z_2_R (f y_1_R x_0_R)) (f z_2_R (f y_1_R x_0_R))) []
* CriticalPair
  Left rule: (f x_3_L y_4_L) -> (f y_4_L x_3_L)
  Right rule: (f (f x_0_R y_1_R) z_2_R) -> (f x_0_R (f y_1_R z_2_R))
  Critical pair: (f (f y_1_R x_0_R) z_2_R) ≈ (f x_0_R (f y_1_R z_2_R))
 which reaches the trivial constrained equation
  (≈ (f (f y_1_R x_0_R) z_2_R) (f x_0_R (f y_1_R z_2_R))) []
	-> (≈ (f (f x_0_R y_1_R) z_2_R) (f x_0_R (f y_1_R z_2_R))) []
	-> (≈ (f x_0_R (f y_1_R z_2_R)) (f x_0_R (f y_1_R z_2_R))) []
 and the trivial constrained equation
  (≈ (f (f y_1_R x_0_R) z_2_R) (f x_0_R (f y_1_R z_2_R))) []
	-> (≈ (f (f y_1_R x_0_R) z_2_R) (f (f y_1_R z_2_R) x_0_R)) []
	-> (≈ (f (f y_1_R x_0_R) z_2_R) (f y_1_R (f z_2_R x_0_R))) []
	-> (≈ (f (f y_1_R x_0_R) z_2_R) (f y_1_R (f x_0_R z_2_R))) []
	-> (≈ (f y_1_R (f x_0_R z_2_R)) (f y_1_R (f x_0_R z_2_R))) []
* CriticalPair
  Left rule: (f (f x_0_L y_1_L) z_2_L) -> (f x_0_L (f y_1_L z_2_L))
  Right rule: (f x_3_R y_4_R) -> (f y_4_R x_3_R)
  Critical pair: (f x_0_L (f y_1_L y_4_R)) ≈ (f y_4_R (f x_0_L y_1_L))
 which reaches the trivial constrained equation
  (≈ (f x_0_L (f y_1_L y_4_R)) (f y_4_R (f x_0_L y_1_L))) []
	-> (≈ (f (f y_1_L y_4_R) x_0_L) (f y_4_R (f x_0_L y_1_L))) []
	-> (≈ (f (f y_4_R y_1_L) x_0_L) (f y_4_R (f x_0_L y_1_L))) []
	-> (≈ (f y_4_R (f y_1_L x_0_L)) (f y_4_R (f x_0_L y_1_L))) []
	-> (≈ (f y_4_R (f y_1_L x_0_L)) (f y_4_R (f y_1_L x_0_L))) []
 and the trivial constrained equation
  (≈ (f x_0_L (f y_1_L y_4_R)) (f y_4_R (f x_0_L y_1_L))) []
	-> (≈ (f x_0_L (f y_1_L y_4_R)) (f (f x_0_L y_1_L) y_4_R)) []
	-> (≈ (f x_0_L (f y_1_L y_4_R)) (f x_0_L (f y_1_L y_4_R))) []


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