; @origtpdbfilename ./TRS/SchneiderKamp/trs/wiehe08.trs
; @xtcfilename "./TRS_Standard/AProVE_07/wiehe08.xml"
(format TRS)
(fun minus 2)
(fun |0| 0)
(fun s 1)
(fun quot 2)
(fun plus 2)
(fun if 3)
(fun gt 2)
(fun not 1)
(fun id 1)
(fun zero 0)
(fun true 0)
(fun false 0)
(rule (minus x |0|) x)
(rule (minus (s x) (s y)) (minus x y))
(rule (quot |0| (s y)) |0|)
(rule (quot (s x) (s y)) (s (quot (minus x y) (s y))))
(rule (plus (s x) (s y)) (s (s (plus (if (gt x y) x y) (if (not (gt x y)) (id x) (id y))))))
(rule (plus (s x) x) (plus (if (gt x x) (id x) (id x)) (s x)))
(rule (plus zero y) y)
(rule (plus (id x) (s y)) (s (plus x (if (gt (s y) y) y (s y)))))
(rule (id x) x)
(rule (if true x y) x)
(rule (if false x y) y)
(rule (not x) (if x false true))
(rule (gt (s x) zero) true)
(rule (gt zero y) false)
(rule (gt (s x) (s y)) (gt x y))