; @origtpdbfilename ./TRS/SchneiderKamp/trs/thiemann34.trs
; @xtcfilename "./TRS_Standard/AProVE_07/thiemann34.xml"
(format TRS)
(fun gt 2)
(fun s 1)
(fun |0| 0)
(fun true 0)
(fun false 0)
(fun divides 2)
(fun div 3)
(fun prime 1)
(fun test 2)
(fun if1 3)
(fun if2 3)
(rule (gt (s x) |0|) true)
(rule (gt |0| y) false)
(rule (gt (s x) (s y)) (gt x y))
(rule (divides x y) (div x y y))
(rule (div |0| |0| z) true)
(rule (div |0| (s x) z) false)
(rule (div (s x) |0| (s z)) (div (s x) (s z) (s z)))
(rule (div (s x) (s y) z) (div x y z))
(rule (prime x) (test x (s (s |0|))))
(rule (test x y) (if1 (gt x y) x y))
(rule (if1 true x y) (if2 (divides x y) x y))
(rule (if1 false x y) true)
(rule (if2 true x y) false)
(rule (if2 false x y) (test x (s y)))