; @origtpdbfilename TRS//AProVE_10/ex4.trs
; @xtcfilename "./TRS_Standard/AProVE_10/ex4.xml"
(format TRS)
(fun add 3)
(fun true 0)
(fun and 2)
(fun isNat 1)
(fun isList 1)
(fun Cons 2)
(fun nil 0)
(fun s 1)
(fun |0| 0)
(fun if 3)
(fun false 0)
(rule (add true x xs) (add (and (isNat x) (isList xs)) x (Cons x xs)))
(rule (isList (Cons x xs)) (isList xs))
(rule (isList nil) true)
(rule (isNat (s x)) (isNat x))
(rule (isNat |0|) true)
(rule (if true x y) x)
(rule (if false x y) y)
(rule (and true true) true)
(rule (and false x) false)
(rule (and x false) false)