; @origtpdbfilename ./TRS/SchneiderKamp/trs/thiemann13.trs
; @xtcfilename "./TRS_Standard/AProVE_07/thiemann13.xml"
(format TRS)
(fun le 2)
(fun |0| 0)
(fun true 0)
(fun s 1)
(fun false 0)
(fun inc 1)
(fun minus 2)
(fun quot 2)
(fun log 1)
(fun log2 2)
(fun if 4)
(fun log_undefined 0)
(fun if2 3)
(rule (le |0| y) true)
(rule (le (s x) |0|) false)
(rule (le (s x) (s y)) (le x y))
(rule (inc |0|) |0|)
(rule (inc (s x)) (s (inc x)))
(rule (minus |0| y) |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 (log x) (log2 x |0|))
(rule (log2 x y) (if (le x |0|) (le x (s |0|)) x (inc y)))
(rule (if true b x y) log_undefined)
(rule (if false b x y) (if2 b x y))
(rule (if2 true x (s y)) y)
(rule (if2 false x y) (log2 (quot x (s (s |0|))) y))