YES

(format LCTRS :logic QF_LIA)
(fun a 0 :sort (Int))
(fun b 0 :sort (Int))
(fun f 2 :sort (Int Int Int))
(fun g 2 :sort (Int Int Int))

(rule (f x_0 y_1) (g a (+ y_1 y_1)) :guard (and (>= y_1 x_0) (= y_1 1)) :vars ((x_0 Int) (y_1 Int)))
(rule (f x_2 y_3) (g b 2) :guard (>= x_2 y_3) :vars ((x_2 Int) (y_3 Int)))
(rule a b)
(rule (g x_4 y_5) (g y_5 x_4) :vars ((x_4 Int) (y_5 Int)))

Confluent by Almost Parallel Closedness with proof:
* CriticalPair
  Left rule: (f x_2_L y_3_L) -> (g b 2) [(>= x_2_L y_3_L)]
  Right rule: (f x_0_R y_1_R) -> (g a (+ y_1_R y_1_R)) [(and (>= y_1_R x_0_R) (= y_1_R 1))]
  Critical pair: (g b 2) ≈ (g a (+ y_1_R y_1_R)) [(and (>= x_0_R y_1_R) (and (>= y_1_R x_0_R) (= y_1_R 1)))]
 which reaches the trivial constrained equation
  (≈ (g b 2) (g a (+ y_1_R y_1_R))) [(and (>= x_0_R y_1_R) (and (>= y_1_R x_0_R) (= y_1_R 1)))]
	-||-> (≈ (g b 2) (g b ?fresh_506)) [(and (>= x_0_R y_1_R) (and (>= y_1_R x_0_R) (= y_1_R 1)) (>= x_0_R y_1_R) (and (>= y_1_R x_0_R) (= y_1_R 1)) (= ?fresh_506 (+ y_1_R y_1_R)))]
* CriticalPair
  Left rule: (f x_0_L y_1_L) -> (g a (+ y_1_L y_1_L)) [(and (>= y_1_L x_0_L) (= y_1_L 1))]
  Right rule: (f x_2_R y_3_R) -> (g b 2) [(>= x_2_R y_3_R)]
  Critical pair: (g a (+ y_3_R y_3_R)) ≈ (g b 2) [(and (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R))]
 which reaches the trivial constrained equation
  (≈ (g a (+ y_3_R y_3_R)) (g b 2)) [(and (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R))]
	-||-> (≈ (g b ?fresh_2431) (g b 2)) [(and (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R) (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R) (= ?fresh_2431 (+ y_3_R y_3_R)))]


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