; @origtpdbfilename ./TRS/higher-order/AotoYam/010.trs
; @xtcfilename "./TRS_Standard/AotoYamada_05/010.xml"
(format TRS)
(fun app 2)
(fun plus 0)
(fun |0| 0)
(fun s 0)
(fun times 0)
(fun curry 0)
(fun map 0)
(fun nil 0)
(fun cons 0)
(fun inc 0)
(fun double 0)
(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 times |0|) y) |0|)
(rule (app (app times (app s x)) y) (app (app plus (app (app times x) y)) y))
(rule (app (app (app curry g) x) y) (app (app g x) 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 inc (app map (app (app curry plus) (app s |0|))))
(rule double (app map (app (app curry times) (app s (app s |0|)))))