Accepted Publications was a reprint publisher, in The Farrell Publishing group, which, I believe, was, at least co-owned by Robert Farrell, who seemed to have a share in Star Publishing, or at least, purchased Star's rights and old stock and plates. It operated in 1957 and 1958, around the same time as Farrell was issuing reprints of Novelty's 1940s Funny Animal comics he'd acquired previously, in Frisky Animals On Parade, and Mighty Bear Comics. The Accepted issue of Animal Adventures 3 is not dated. I strongly believe it is a reprint of Timor's 1954 issue. Why would Timor farm Issue #2 out to Accepted, after starting their new, first Funny Animal series, and then bring it back for Issue #3, and then Accepted re-issued it in the same year??? The Animal adventures #2 issue we have here at CB+ is also an Accepted, non-dated issue, which is listed as 1958 (according to Grand Comics Database). So, I think that all 3 issues of this title came out originally in 1953(#1) and 1954(#2-3), and were all reprinted by Accepted Comics in 1957-58.
Link to the book:
Animal Adventures 3