YES

(format LCTRS :logic QF_LIA)
(fun sum1 1 :sort (Int Int))

(rule (sum1 x_0) (+ x_0 (sum1 (- x_0 1))) :guard (<= 0 (- x_0 1)) :vars ((x_0 Int)))
(rule (sum1 x_1) 0 :guard (<= x_1 0) :vars ((x_1 Int)))

Confluent by Orthogonality with proof:
no critical pairs

Elapsed Time:  27.85 ms