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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)) (+ 1 (length ?l))) :rewrite-rule)))
(declare-fun gen_cons (Int list) list)
(assert (forall ((?n Int) (?l list)) (! (=> (= ?n 0) (= (gen_cons ?n ?l) ?l)) :rewrite-rule)))
(assert (forall ((?n Int) (?l list)) (! (=> (> ?n 0) (= (gen_cons ?n ?l)
(gen_cons (- ?n 1) (cons 1 ?l)))) :rewrite-rule)))
;;(assert (not (forall ((?n Int)) (=> (>= ?n 0) (=> (= (length (gen_cons ?n nil)) ?n) (= (length (gen_cons (+ ?n 1) nil)) (+ ?n 1))) ))))
;;(assert (not (forall ((?n Int) (?l list)) (=> (>= ?n 0) (=> (= (length ?l) ?n) (= (length (cons 1 ?l)) (+ ?n 1))) ))))
;; (assert (not (forall ((?n Int)) (=> (>= ?n 0) (=> (= (length (gen_cons ?n nil)) ?n) (= (length (cons 1 (gen_cons ?n nil))) (+ ?n 1))) ))))
;;(assert (not (forall ((?n Int)) (=> (>= ?n 0) (= (gen_cons (+ ?n 1) nil) (cons 1 (gen_cons ?n nil))) ))))
(assert (not (forall ((?n Int)) (=> (>= ?n 0) (=>
(forall ((?l list)) (= (gen_cons ?n (cons 1 ?l)) (cons 1 (gen_cons ?n ?l))))
(forall ((?l list)) (= (gen_cons (+ ?n 1) (cons 1 ?l)) (cons 1 (gen_cons (+ ?n 1) ?l))))
)))))
(check-sat)
(exit)
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