; @origtpdbfilename ./TRS/SchneiderKamp/trs/thiemann16.trs
; @xtcfilename "./TRS_Standard/AProVE_07/thiemann16.xml"
(format TRS)
(fun check 1)
(fun |0| 0)
(fun zero 0)
(fun s 1)
(fun odd 0)
(fun even 0)
(fun half 1)
(fun plus 2)
(fun times 2)
(fun timesIter 3)
(fun if 5)
(fun p 1)
(rule (check |0|) zero)
(rule (check (s |0|)) odd)
(rule (check (s (s |0|))) even)
(rule (check (s (s (s x)))) (check (s x)))
(rule (half |0|) |0|)
(rule (half (s |0|)) |0|)
(rule (half (s (s x))) (s (half x)))
(rule (plus |0| y) y)
(rule (plus (s x) y) (s (plus x y)))
(rule (times x y) (timesIter x y |0|))
(rule (timesIter x y z) (if (check x) x y z (plus z y)))
(rule (p (s x)) x)
(rule (p |0|) |0|)
(rule (if zero x y z u) z)
(rule (if odd x y z u) (timesIter (p x) y u))
(rule (if even x y z u) (plus (timesIter (half x) y (half z)) (timesIter (half x) y (half (s z)))))