YES

(format LCTRS :logic QF_LIA)
(fun a 0 :sort (Int))
(fun f 1 :sort (Int Int))
(fun g 1 :sort (Int Int))

(rule (f x_0) (g y_1) :vars ((x_0 Int) (y_1 Int)))
(rule (g y_2) a :guard (= y_2 y_2) :vars ((y_2 Int)))

Confluent by Almost Parallel Closedness with proof:
* CriticalPair
  Left rule: (f x_0_L) -> (g y_1_L)
  Right rule: (f x_0_R) -> (g y_1_R)
  Critical pair: (g y_1_L) ≈ (g y_1_R) [(and (= y_1_L y_1_L) (= y_1_R y_1_R))]
 which reaches the trivial constrained equation
  (≈ (g y_1_L) (g y_1_R)) [(and (= y_1_L y_1_L) (= y_1_R y_1_R))]
	-||-> (≈ a (g y_1_R)) [(and (= y_1_L y_1_L) (= y_1_R y_1_R))]
	-||-> (≈ a a) [(and (= y_1_L y_1_L) (= y_1_R y_1_R))]


Elapsed Time:  39.94 ms