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;; Same than length.smt2 but the nil case is not a rewrite rule
;; So here the rewrite rules have no guards length
(set-logic AUFLIA)
(set-info :status unsat)
;; don't use a datatypes for currently focusing in uf
(declare-sort list 0)
(declare-fun cons (Int list) list)
(declare-fun nil () list)
;;define length
(declare-fun length (list) Int)
(assert (= (length nil) 0))
(assert (forall ((?e Int) (?l list)) (! (= (length (cons ?e ?l)) (+ (length ?l) 1)) :rewrite-rule)))
;;(assert (forall ((?l list)) (=> (= ?l nil) (= (length ?l) 0))))
;;(assert (forall ((?e Int) (?l list) (?l2 list)) (=> (= ?l2 (cons ?e ?l)) (= (length ?l2) (+ (length ?l) 1)))))
(assert (forall ((?a Int) (?b Int) (?l list))
(not (> (length (cons ?a (cons ?b ?l))) (length ?l)))))
(check-sat)
(exit)
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