; @origtpdbfilename ./TRS/Thiemann/factorial2.trs
; @xtcfilename "./TRS_Standard/AProVE_06/factorial2.xml"
(format TRS)
(fun plus 2)
(fun |0| 0)
(fun s 1)
(fun times 2)
(fun p 1)
(fun minus 2)
(fun isZero 1)
(fun true 0)
(fun false 0)
(fun facIter 2)
(fun if 4)
(fun factorial 1)
(rule (plus |0| x) x)
(rule (plus (s x) y) (s (plus x y)))
(rule (times |0| y) |0|)
(rule (times (s x) y) (plus y (times x y)))
(rule (p (s x)) x)
(rule (p |0|) |0|)
(rule (minus x |0|) x)
(rule (minus |0| x) |0|)
(rule (minus x (s y)) (p (minus x y)))
(rule (isZero |0|) true)
(rule (isZero (s x)) false)
(rule (facIter x y) (if (isZero x) (minus x (s |0|)) y (times y x)))
(rule (if true x y z) y)
(rule (if false x y z) (facIter x z))
(rule (factorial x) (facIter x (s |0|)))