; @origtpdbfilename ./TRS/aprove08/parting02_doublelist.trs
; @xtcfilename "./TRS_Standard/AProVE_08/parting02_doublelist.xml"
(format TRS)
(fun double 1)
(fun |0| 0)
(fun s 1)
(fun del 2)
(fun nil 0)
(fun cons 2)
(fun if 4)
(fun eq 2)
(fun true 0)
(fun false 0)
(fun first 1)
(fun doublelist 1)
(rule (double |0|) |0|)
(rule (double (s x)) (s (s (double x))))
(rule (del x nil) nil)
(rule (del x (cons y xs)) (if (eq x y) x y xs))
(rule (if true x y xs) xs)
(rule (if false x y xs) (cons y (del x xs)))
(rule (eq |0| |0|) true)
(rule (eq |0| (s y)) false)
(rule (eq (s x) |0|) false)
(rule (eq (s x) (s y)) (eq x y))
(rule (first nil) |0|)
(rule (first (cons x xs)) x)
(rule (doublelist nil) nil)
(rule (doublelist (cons x xs)) (cons (double x) (doublelist (del (first (cons x xs)) (cons x xs)))))