; @xtcfilename "./TRS_Standard/Mixed_TRS/div_hard.xml"
(format TRS)
(fun double 1)
(fun plus 2)
(fun |0| 0)
(fun s 1)
(fun minus 2)
(fun div 2)
(rule (double x) (plus x x))
(rule (double |0|) |0|)
(rule (double (s x)) (s (s (double x))))
(rule (plus |0| y) y)
(rule (plus (s x) y) (s (plus x y)))
(rule (minus (s x) (s y)) (minus x y))
(rule (minus |0| x) |0|)
(rule (minus x |0|) x)
(rule (div (s x) (s y)) (s (div (minus (s x) (double (s y))) (s y))))
(rule (div |0| (s y)) |0|)