; @origtpdbfilename ./TRS/SchneiderKamp/trs/otto11.trs
; @xtcfilename "./TRS_Standard/AProVE_07/otto11.xml"
(format TRS)
(fun times 2)
(fun help 3)
(fun |0| 0)
(fun if 4)
(fun lt 2)
(fun true 0)
(fun plus 2)
(fun s 1)
(fun false 0)
(rule (times x y) (help x y |0|))
(rule (help x y c) (if (lt c y) x y c))
(rule (if true x y c) (plus x (help x y (s c))))
(rule (if false x y c) |0|)
(rule (lt |0| (s x)) true)
(rule (lt (s x) |0|) false)
(rule (lt (s x) (s y)) (lt x y))
(rule (plus x |0|) x)
(rule (plus |0| x) x)
(rule (plus x (s y)) (s (plus x y)))
(rule (plus (s x) y) (s (plus x y)))