; @origtpdbfilename ./TRS/currying/Ste92/perfect.trs
; @xtcfilename "./TRS_Standard/Applicative_first_order_05/perfect.xml"
(format TRS)
(fun app 2)
(fun perfectp 0)
(fun |0| 0)
(fun false 0)
(fun s 0)
(fun f 0)
(fun true 0)
(fun minus 0)
(fun if 0)
(fun le 0)
(fun map 0)
(fun nil 0)
(fun cons 0)
(fun filter 0)
(fun filter2 0)
(rule (app perfectp |0|) false)
(rule (app perfectp (app s x)) (app (app (app (app f x) (app s |0|)) (app s x)) (app s x)))
(rule (app (app (app (app f |0|) y) |0|) u) true)
(rule (app (app (app (app f |0|) y) (app s z)) u) false)
(rule (app (app (app (app f (app s x)) |0|) z) u) (app (app (app (app f x) u) (app (app minus z) (app s x))) u))
(rule (app (app (app (app f (app s x)) (app s y)) z) u) (app (app (app if (app (app le x) y)) (app (app (app (app f (app s x)) (app (app minus y) x)) z) u)) (app (app (app (app f x) u) z) u)))
(rule (app (app map |fun|) nil) nil)
(rule (app (app map |fun|) (app (app cons x) xs)) (app (app cons (app |fun| x)) (app (app map |fun|) xs)))
(rule (app (app filter |fun|) nil) nil)
(rule (app (app filter |fun|) (app (app cons x) xs)) (app (app (app (app filter2 (app |fun| x)) |fun|) x) xs))
(rule (app (app (app (app filter2 true) |fun|) x) xs) (app (app cons x) (app (app filter |fun|) xs)))
(rule (app (app (app (app filter2 false) |fun|) x) xs) (app (app filter |fun|) xs))