; @origtpdbfilename ./TRS/currying/AG01/#3.40.trs
; @xtcfilename "./TRS_Standard/Applicative_first_order_05/#3.40.xml"
(format TRS)
(fun app 2)
(fun minus 0)
(fun |0| 0)
(fun s 0)
(fun quot 0)
(fun plus 0)
(fun map 0)
(fun nil 0)
(fun cons 0)
(fun filter 0)
(fun filter2 0)
(fun true 0)
(fun false 0)
(rule (app (app minus x) |0|) x)
(rule (app (app minus (app s x)) (app s y)) (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 plus |0|) y) y)
(rule (app (app plus (app s x)) y) (app s (app (app plus x) y)))
(rule (app (app plus (app (app minus x) (app s |0|))) (app (app minus y) (app s (app s z)))) (app (app plus (app (app minus y) (app s (app s z)))) (app (app minus x) (app s |0|))))
(rule (app (app plus (app (app plus x) (app s |0|))) (app (app plus y) (app s (app s z)))) (app (app plus (app (app plus y) (app s (app s z)))) (app (app plus x) (app s |0|))))
(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))