YES

(format LCTRS :logic QF_LIA)
(fun f2 2 :sort (Int Int Int))
(fun u_25 1 :sort (Int Int))
(fun u_31 2 :sort (Int Int Int))
(fun u_34 1 :sort (Int Int))

(rule (u_34 w_10_0) w_10_0 :vars ((w_10_0 Int)))
(rule (u_31 m_1 w_9_2) (u_34 (f2 (- m_1 1) w_9_2)) :vars ((m_1 Int) (w_9_2 Int)))
(rule (u_25 w_8_3) w_8_3 :vars ((w_8_3 Int)))
(rule (f2 m_4 n_5) (u_31 m_4 (f2 m_4 (- n_5 1))) :guard (and (or (<= m_4 0) (distinct n_5 0)) (distinct m_4 0)) :vars ((m_4 Int) (n_5 Int)))
(rule (f2 m_6 n_7) (+ n_7 1) :guard (and (or (<= m_6 0) (distinct n_7 0)) (= m_6 0)) :vars ((m_6 Int) (n_7 Int)))
(rule (f2 m_8 n_9) (u_25 (f2 (- m_8 1) 1)) :guard (and (> m_8 0) (= n_9 0)) :vars ((m_8 Int) (n_9 Int)))

Confluent by Almost Parallel Closedness with proof:
no critical pairs

Elapsed Time:  33.37 ms