; @origtpdbfilename ./TRS/currying/AG01/#3.2.trs
; @xtcfilename "./TRS_Standard/Applicative_first_order_05/#3.2.xml"
(format TRS)
(fun app 2)
(fun pred 0)
(fun s 0)
(fun minus 0)
(fun |0| 0)
(fun quot 0)
(fun map 0)
(fun nil 0)
(fun cons 0)
(fun filter 0)
(fun filter2 0)
(fun true 0)
(fun false 0)
(rule (app pred (app s x)) x)
(rule (app (app minus x) |0|) x)
(rule (app (app minus x) (app s y)) (app pred (app (app minus x) y)))
(rule (app (app quot |0|) (app s y)) |0|)
(rule (app (app quot (app s x)) (app s y)) (app s (app (app quot (app (app minus x) y)) (app s y))))
(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))