; @origtpdbfilename ./AProVE_09_Inductive/minsort.trs
; @xtcfilename "./TRS_Standard/AProVE_09_Inductive/minsort.xml"
(format TRS)
(fun le 2)
(fun |0| 0)
(fun true 0)
(fun s 1)
(fun false 0)
(fun eq 2)
(fun minsort 1)
(fun nil 0)
(fun cons 2)
(fun min 1)
(fun rm 2)
(fun if1 4)
(fun if2 4)
(rule (le |0| y) true)
(rule (le (s x) |0|) false)
(rule (le (s x) (s y)) (le x y))
(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 (minsort nil) nil)
(rule (minsort (cons x xs)) (cons (min (cons x xs)) (minsort (rm (min (cons x xs)) (cons x xs)))))
(rule (min nil) |0|)
(rule (min (cons x nil)) x)
(rule (min (cons x (cons y xs))) (if1 (le x y) x y xs))
(rule (if1 true x y xs) (min (cons x xs)))
(rule (if1 false x y xs) (min (cons y xs)))
(rule (rm x nil) nil)
(rule (rm x (cons y xs)) (if2 (eq x y) x y xs))
(rule (if2 true x y xs) (rm x xs))
(rule (if2 false x y xs) (cons y (rm x xs)))