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))
(fun h 1 :sort (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 (h (f x_2 y_3)) (h (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 Parallel Closedness with proof:
* 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: (h (f x_2_R y_3_R)) -> (h (g b 2)) [(and (>= x_2_R y_3_R) (>= x_2_R y_3_R))]
  Critical pair: (h (g a (+ y_3_R y_3_R))) ≈ (h (g b 2)) [(and (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R) (>= x_2_R y_3_R))]
 which reaches the trivial constrained equation
  (≈ (h (g a (+ y_3_R y_3_R))) (h (g b 2))) [(and (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R) (>= x_2_R y_3_R))]
	-||-> (≈ (h (g b ?fresh_396)) (h (g b 2))) [(and (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R) (>= x_2_R y_3_R) (and (>= y_3_R x_2_R) (= y_3_R 1)) (>= x_2_R y_3_R) (>= x_2_R y_3_R) (= ?fresh_396 (+ y_3_R y_3_R)))]


Elapsed Time:  15.70 ms