YES

(format LCTRS :logic QF_LIA)
(fun g1 1 :sort (Int Int))
(fun triangle1 1 :sort (Int Int))
(fun u_2 1 :sort (Int Int))
(fun u_9 2 :sort (Int Int Int))

(rule (u_9 n_0 w_4_1) (+ n_0 w_4_1) :vars ((n_0 Int) (w_4_1 Int)))
(rule (g1 n_2) (u_9 n_2 (g1 (- n_2 1))) :guard (> n_2 0) :vars ((n_2 Int)))
(rule (g1 n_3) 0 :guard (<= n_3 0) :vars ((n_3 Int)))
(rule (u_2 w_2_4) w_2_4 :vars ((w_2_4 Int)))
(rule (triangle1 n_5) (u_2 (g1 n_5)) :vars ((n_5 Int)))

Confluent by Parallel Closedness with proof:
no critical pairs

Elapsed Time:  29.06 ms