EASTERBROOK, Circuit Judge.

An employer that withdraws from an underfunded pension plan must cover its share of the shortfall. 29 U.S.C. §§ 1381, 1391. After concluding that Allega Concrete had withdrawn, the Central States Pension Fund sent it a bill for about $375,000. The Multiemployer Pension Plan Amendments Act of 1980 (MPPAA) gives an employer 90 days to ask a pension plan to review its decision. 29 U.S.C. § 1399(b)(2)(A). If the plan adheres to the original decision — or if it does not act within 120 days — the employer has a further 60 days to seek arbitration. 29 U.S.C. § 1401(a)(1). For Allega, the last day was July 16, 2013.

On July 9 Allega sent the Fund a letter demanding arbitration. It followed up on July 29 with a notice to the American Arbitration Association. Problem: The AAA's rules require that notices go to both the pension administrator and the AAA. Privately adopted dispute-resolution rules require the approval of the Pension Benefit Guaranty Corporation. 29 U.S.C. § 1401(a)(2); 29 C.F.R. § 4221.14(a). In 1985 the PBGC approved the AAA's rules for arbitration under the MPPAA, 50 Fed. Reg. 38,046 (Sept. 19, 1985), and in 1986 it approved some amendments, 51 Fed.Reg. 22,585 (June 20, 1986). The Fund has adopted those rules, but Allega did not notify the AAA within the statutory time limit.

The district court concluded that Allega had waited too long to seek arbitration and must pay withdrawal liability as the Fund calculated it. 2014 WL 2598816, 2014 U.S. Dist. LEXIS 78998 (N.D.Ill. June 10, 2014). It relied on § 7 of the AAA's rules, which provides in part:

Allega concedes that it did not do what § 7 requires. It contends that it did not need to do so because some of the AAA's and the Fund's procedures and requirements have not been submitted to or approved by the PBGC.

In February 2013 the AAA raised the fees that must accompany a demand for arbitration. (These fees appear in the "Administrative Fee Schedule" to which § 7(a)(ii) refers.) The schedule in force in 1985 called for $650 with any demand for arbitration; as amended in 2013, the schedule specifies an initial payment of $4,350 and a "final payment" (due at the arbitration's close) of $1,750, for a total of $6,100. (Cases with larger stakes may require higher fees; the numbers we've given are what Allega would have been required to pay.) The Fund's rules provide that arbitration will be conducted in Chicago (the Fund's home base), while § 8 of the AAA's rules says that the parties and the arbitrator will select a venue jointly, with the arbitrator to decide if the parties cannot agree. See also 29 C.F.R. § 4221.6. The Fund also calls for an award of attorneys' fees in its favor if it prevails. Section 38 of the AAA's rules, by contrast, gives the arbitrator discretion whether to award fees. See also 29 C.F.R. § 4221.10(c).

According to Allega, these provisions relieve it of any obligation to serve the AAA with the demand for arbitration. But why? Let us suppose that both the AAA's higher fees and the differences between the Fund's rules and the AAA's required the PBGC's approval. (That may or may not be true; we need not decide. If it is true, then any conflict between the AAA's approved rules and the unilaterally adopted regulations of the Fund would be resolved in favor of the AAA's rules.) The fact remains that the PBGC did approve the AAA's rules in 1985 and 1986. It is the approved rules that call for the demand to be sent to the AAA (as well as the Fund) during the 60 days allowed by statute.

If Allega had sent a timely demand to the AAA, together with a check for $650, and the AAA had refused to proceed with arbitration, then we might have to decide whether an amendment of the fee schedule requires the PBGC's approval. But that's not what happened. And because Allega did not make a timely demand for arbitration, questions about venue and legal fees never arose. They could have been reviewed by the district court on a petition to review an arbitrator's final decision; any dispute about the AAA's fees could have been reviewed the same way. But Allega did not take the essential first step: a timely demand for arbitration sent to the AAA.

Allega does not contend that the Fund needed the PBGC's approval to adopt the AAA's rules. Nor does it contend that, if the AAA's rules apply, its demand for arbitration was effective nonetheless. That is, Allega does not maintain that notice to the Fund but not the AAA suffices. It does argue that the Fund's failure to act within 120 days on its request for reconsideration tolls the time to seek arbitration, but that contention boils down to disagreement with the statutory rule that the 60 days to demand arbitration begins to run when 120 days have passed without action. The district court's judgment therefore is

AFFIRMED.