YES

(format LCTRS :logic QF_LIA)
(fun badfib 1 :sort (Int Unit))
(fun return 1 :sort (Int Unit))
(fun w2 2 :sort (Unit Unit Unit))

(rule (w2 (return x_0) (return y_1)) (return (+ x_0 y_1)) :vars ((x_0 Int) (y_1 Int)))
(rule (badfib x_2) (w2 (badfib (- x_2 1)) (badfib (- x_2 2))) :guard (> x_2 1) :vars ((x_2 Int)))
(rule (badfib x_3) (return 1) :guard (= x_3 1) :vars ((x_3 Int)))
(rule (badfib x_4) (return 1) :guard (<= x_4 0) :vars ((x_4 Int)))

Confluent by Orthogonality with proof:
no critical pairs

Elapsed Time:  16.31 ms