YES

(format LCTRS :logic QF_LIA)
(fun fib 1 :sort (Int Int))
(fun fib1 1 :sort (Int Int))
(fun u 4 :sort (Int Int Int Int Int))

(rule (fib x_0) (+ (fib (- x_0 1)) (fib (- x_0 2))) :guard (>= (- x_0 2) 0) :vars ((x_0 Int)))
(rule (fib 1) 1)
(rule (fib x_1) 0 :guard (<= x_1 0) :vars ((x_1 Int)))
(rule (u x_2 i_3 y_4 z_5) y_4 :guard (not (>= x_2 i_3)) :vars ((x_2 Int) (i_3 Int) (y_4 Int) (z_5 Int)))
(rule (u x_6 i_7 y_8 z_9) (u x_6 (+ i_7 1) z_9 (+ y_8 z_9)) :guard (>= x_6 i_7) :vars ((x_6 Int) (i_7 Int) (y_8 Int) (z_9 Int)))
(rule (fib1 x_10) (u x_10 1 0 1) :vars ((x_10 Int)))

Confluent by Parallel Closedness with proof:
no critical pairs

Elapsed Time:   8.55 ms