; @origtpdbfilename ./TRS/AProVE/IJCAR_26.trs
; @xtcfilename "./TRS_Standard/AProVE_04/IJCAR_26.xml"
(format TRS)
(fun p 1)
(fun s 1)
(fun plus 2)
(fun |0| 0)
(fun times 2)
(fun div 2)
(fun quot 3)
(fun eq 2)
(fun true 0)
(fun false 0)
(fun divides 2)
(fun prime 1)
(fun pr 2)
(fun if 3)
(rule (p (s x)) x)
(rule (plus x |0|) x)
(rule (plus |0| y) y)
(rule (plus (s x) y) (s (plus x y)))
(rule (plus (s x) y) (s (plus (p (s x)) y)))
(rule (plus x (s y)) (s (plus x (p (s y)))))
(rule (times |0| y) |0|)
(rule (times (s |0|) y) y)
(rule (times (s x) y) (plus y (times x y)))
(rule (div |0| y) |0|)
(rule (div x y) (quot x y y))
(rule (quot |0| (s y) z) |0|)
(rule (quot (s x) (s y) z) (quot x y z))
(rule (quot x |0| (s z)) (s (div x (s z))))
(rule (div (div x y) z) (div x (times y z)))
(rule (eq |0| |0|) true)
(rule (eq (s x) |0|) false)
(rule (eq |0| (s y)) false)
(rule (eq (s x) (s y)) (eq x y))
(rule (divides y x) (eq x (times (div x y) y)))
(rule (prime (s (s x))) (pr (s (s x)) (s x)))
(rule (pr x (s |0|)) true)
(rule (pr x (s (s y))) (if (divides (s (s y)) x) x (s y)))
(rule (if true x y) false)
(rule (if false x y) (pr x y))