YES

(format LCTRS :logic QF_LIA)
(fun proc_G 1 :sort (Int result_proc))
(fun return_proc 1 :sort (Int result_proc))
(fun v 2 :sort (Int result_proc result_proc))

(rule (v n_0 (return_proc m_1)) (return_proc (+ n_0 m_1)) :vars ((n_0 Int) (m_1 Int)))
(rule (proc_G n_2) (v n_2 (proc_G (- n_2 1))) :guard (> n_2 1) :vars ((n_2 Int)))
(rule (proc_G n_3) (return_proc n_3) :guard (<= n_3 1) :vars ((n_3 Int)))

Confluent by Parallel Closedness with proof:
no critical pairs

Elapsed Time:  14.14 ms