YES

(format LCTRS :logic QF_LIA)
(fun return 1 :sort (Int Unit))
(fun sum2 2 :sort (Int Int Unit))
(fun u 3 :sort (Int Int Int Unit))

(rule (u m_0 n_1 count_2) (return count_2) :guard (not (<= m_0 n_1)) :vars ((m_0 Int) (n_1 Int) (count_2 Int)))
(rule (u m_3 n_4 count_5) (u (+ m_3 1) n_4 (+ count_5 m_3)) :guard (<= m_3 n_4) :vars ((m_3 Int) (n_4 Int) (count_5 Int)))
(rule (sum2 m_6 n_7) (u m_6 n_7 0) :vars ((m_6 Int) (n_7 Int)))

Confluent by Parallel Closedness with proof:
no critical pairs

Elapsed Time:   9.61 ms