YES

(format LCTRS :logic QF_LRA)
(fun sqrt 1 :sort (Real Real))
(fun sumroot 1 :sort (Real Real))

(rule (sumroot x_0) 0 :guard (>= 0 x_0) :vars ((x_0 Real)))
(rule (sumroot x_1) (+ (sqrt x_1) (sumroot (- x_1 1))) :guard (not (>= 0 x_1)) :vars ((x_1 Real)))

Confluent by Weak Orthogonality with proof:
no critical pairs

Elapsed Time:  14.27 ms