; @origtpdbfilename ./TRS/currying/AG01/#3.38.trs
; @xtcfilename "./TRS_Standard/Applicative_first_order_05/#3.38.xml"
(format TRS)
(fun app 2)
(fun rev 0)
(fun nil 0)
(fun cons 0)
(fun rev1 0)
(fun rev2 0)
(fun |0| 0)
(fun s 0)
(fun map 0)
(fun filter 0)
(fun filter2 0)
(fun true 0)
(fun false 0)
(rule (app rev nil) nil)
(rule (app rev (app (app cons x) l)) (app (app cons (app (app rev1 x) l)) (app (app rev2 x) l)))
(rule (app (app rev1 |0|) nil) |0|)
(rule (app (app rev1 (app s x)) nil) (app s x))
(rule (app (app rev1 x) (app (app cons y) l)) (app (app rev1 y) l))
(rule (app (app rev2 x) nil) nil)
(rule (app (app rev2 x) (app (app cons y) l)) (app rev (app (app cons x) (app (app rev2 y) l))))
(rule (app (app map f) nil) nil)
(rule (app (app map f) (app (app cons x) xs)) (app (app cons (app f x)) (app (app map f) xs)))
(rule (app (app filter f) nil) nil)
(rule (app (app filter f) (app (app cons x) xs)) (app (app (app (app filter2 (app f x)) f) x) xs))
(rule (app (app (app (app filter2 true) f) x) xs) (app (app cons x) (app (app filter f) xs)))
(rule (app (app (app (app filter2 false) f) x) xs) (app (app filter f) xs))