; @origtpdbfilename ./TRS/higher-order/Bird/TreeHeight.trs
; @xtcfilename "./TRS_Standard/Applicative_05/TreeHeight.xml"
(format TRS)
(fun app 2)
(fun map 0)
(fun nil 0)
(fun cons 0)
(fun le 0)
(fun |0| 0)
(fun true 0)
(fun s 0)
(fun false 0)
(fun maxlist 0)
(fun if 0)
(fun height 0)
(fun node 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 le |0|) y) true)
(rule (app (app le (app s x)) |0|) false)
(rule (app (app le (app s x)) (app s y)) (app (app le x) y))
(rule (app (app maxlist x) (app (app cons y) ys)) (app (app if (app (app le x) y)) (app (app maxlist y) ys)))
(rule (app (app maxlist x) nil) x)
(rule (app height (app (app node x) xs)) (app s (app (app maxlist |0|) (app (app map height) xs))))