; @origtpdbfilename ./TRS/SchneiderKamp/trs/wiehe12.trs
; @xtcfilename "./TRS_Standard/AProVE_07/wiehe12.xml"
(format TRS)
(fun g 2)
(fun s 1)
(fun if 3)
(fun and 2)
(fun f 1)
(fun t 1)
(fun k 2)
(fun minus 2)
(fun m 2)
(fun n 2)
(fun |0| 0)
(fun p 2)
(fun gt 2)
(fun not 1)
(fun id 1)
(fun true 0)
(fun false 0)
(fun h 1)
(rule (g (s x) (s y)) (if (and (f (s x)) (f (s y))) (t (g (k (minus (m x y) (n x y)) (s (s |0|))) (k (n (s x) (s y)) (s (s |0|))))) (g (minus (m x y) (n x y)) (n (s x) (s y)))))
(rule (n |0| y) |0|)
(rule (n x |0|) |0|)
(rule (n (s x) (s y)) (s (n x y)))
(rule (m |0| y) y)
(rule (m x |0|) x)
(rule (m (s x) (s y)) (s (m x y)))
(rule (k |0| (s y)) |0|)
(rule (k (s x) (s y)) (s (k (minus x y) (s y))))
(rule (t x) (p x x))
(rule (p (s x) (s y)) (s (s (p (if (gt x y) x y) (if (not (gt x y)) (id x) (id y))))))
(rule (p (s x) x) (p (if (gt x x) (id x) (id x)) (s x)))
(rule (p |0| y) y)
(rule (p (id x) (s y)) (s (p x (if (gt (s y) y) y (s y)))))
(rule (minus x |0|) x)
(rule (minus (s x) (s y)) (minus x 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 (and x false) false)
(rule (and true true) true)
(rule (f |0|) true)
(rule (f (s x)) (h x))
(rule (h |0|) false)
(rule (h (s x)) (f x))
(rule (gt (s x) |0|) true)
(rule (gt |0| y) false)
(rule (gt (s x) (s y)) (gt x y))