; @origtpdbfilename ./TRS/SchneiderKamp/trs/thiemann26.trs
; @xtcfilename "./TRS_Standard/AProVE_07/thiemann26.xml"
(format TRS)
(fun ge 2)
(fun |0| 0)
(fun true 0)
(fun s 1)
(fun false 0)
(fun minus 2)
(fun id_inc 1)
(fun quot 2)
(fun div 3)
(fun if 5)
(fun div_by_zero 0)
(rule (ge x |0|) true)
(rule (ge |0| (s y)) false)
(rule (ge (s x) (s y)) (ge x y))
(rule (minus x |0|) x)
(rule (minus |0| y) |0|)
(rule (minus (s x) (s y)) (minus x y))
(rule (id_inc x) x)
(rule (id_inc x) (s x))
(rule (quot x y) (div x y |0|))
(rule (div x y z) (if (ge y (s |0|)) (ge x y) x y z))
(rule (if false b x y z) div_by_zero)
(rule (if true false x y z) z)
(rule (if true true x y z) (div (minus x y) y (id_inc z)))