YES

(format LCTRS :logic QF_LIA)
(fun f1 1 :sort (Int Int))
(fun u_1 1 :sort (Int Int))
(fun u_6 1 :sort (Int Int))

(rule (u_6 x_0) x_0 :guard (>= x_0 0) :vars ((x_0 Int)))
(rule (u_6 x_1) 0 :guard (< x_1 0) :vars ((x_1 Int)))
(rule (f1 x_2) (u_6 x_2) :guard (<= x_2 0) :vars ((x_2 Int)))
(rule (u_1 w_1_3) (u_6 (+ w_1_3 1)) :vars ((w_1_3 Int)))
(rule (f1 x_4) (u_1 (f1 (- x_4 1))) :guard (> x_4 0) :vars ((x_4 Int)))

Confluent by Weak Orthogonality with proof:
no critical pairs

Elapsed Time:  14.62 ms