; @author Jonas Schöpf
; Ctrl example from examples/student/fib09.ctrs
(format LCTRS :smtlib 2.6)

(theory Ints)

(sort Unit)

(fun p (-> Int Int Int Int Int Unit))
(fun return (-> Int Unit))
(fun w (-> Int Int Int Int Int Unit))
(fun v (-> Int Int Int Int Int Unit))
(fun u (-> Int Int Int Int Int Unit))
(fun fastfib (-> Int Unit))

(rule (p n x y z i) (return x) :guard (not (< i n)))
(rule (p n x y z i) (p n (+ x y) x x (+ i 1)) :guard (< i n))
(rule (w n x y z i) (p n x y z 1) :guard (not (> n 46)))
(rule (w n x y z i) (return -1) :guard (> n 46))
(rule (v n x y z i) (return n) :guard (not (< n 0)))
(rule (v n x y z i) (return 0) :guard (< n 0))
(rule (u n x y z i) (w n x y z i) :guard (not (<= n 1)))
(rule (u n x y z i) (v n x y z i) :guard (<= n 1))
(rule (fastfib n) (u n 1 0 rnd3 rnd4))