BACKGROUND
PER CURIAM.Plaintiff-appellant Thyssen, Inc. (“Thys-sen”) contracted for a cargo of steel coils and the cargo’s delivery • to the United States with a Hong Kong company, Me-talsrussia, on October 26, 1996. Delivery was to be completed by January 31, 1997. Metalsrussia arranged to ship the coils by subchartering the MARKOS N from Western Bulk Carriers, which had previously chartered the ship from its owner, Defendant-appellee Calypso Shipping Corp., S.A. (“Calypso”).1 The MARKOS N charter agreement (or charter party) between Me-talsrussia and Western Bulk Carrier is at the center of this dispute.
Two bills of lading issued for Thyssen’s cargo from an agent of Western Bulk Carriers on January 23 and 24,1997, referencing the above-mentioned charter party. Both bills of lading contain, as the first condition of carriage, the provision: “All terms and conditions, liberties and exceptions to the Charter Party, dated as overleaf, including the Law and Arbitration Clause, are herewith incorporated.”
When the coils arrived in the United States, they were damaged by rust. Despite the damage, Western Bulk Carriers was paid by Metalsrussia, which was in turn paid in full by Thyssen. The dispute now is between Thyssen and the vessel’s owners and managers and the ship itself in rem.
Thyssen brought suit in the Southern District of Texas on March 5, 1997, which issued a warrant for the arrest of the MARKOS N and ordered expedited discovery to allow inspection of the vessel. In exchange for the release of the ship, Thyssen accepted a “Club Letter of Undertaking” from the vessel’s insurer, which promised to pay up to $600,000 in the event of a final judgment for the plaintiff. The letter reserved all defenses.
The parties agreed to transfer the action to the Southern District of New York in August of 1997. On March 11, 1998, a little more than one year after the alleged damage took place, Calypso filed an answer on behalf of itself and the vessel. *104The answer raised a number of defenses, including a claim that its liability was limited to $500 per package under the Carriage of Goods by Sea Act (“COGSA”). The answer did not mention the arbitration clause. In November 1998, Thyssen, seeking to dismiss defendant’s per-package defense, moved for partial summary judgment. In response, Calypso filed its opposition to Thyssen’s motion and, arguing that the incorporated bill of lading required that disputes be resolved by arbitration in London under English law, made a cross-motion to stay the proceedings pursuant to the Federal Arbitration Act.
The district court (Mukasey, J.) stayed the federal court proceedings. It found (1) that Thyssen’s bill of lading incorporated the London arbitration clause of the MAR-EOS N charter party between Western Bulk Carriers and Metalsrussia; (2) that there was adequate evidence of the incorporation by reference of a written arbitration provision into the charter party; (3) that the charter party contained a “broad” arbitration clause sufficient to bind nonsig-natories; (4) that Thyssen’s in rem action against the vessel was arbitrable; (5) that Calypso had not waived its right to arbitrate the dispute by allowing the litigation to proceed; and (6) that whether Thys-sen’s claims were time-barred was a matter for the arbitrator to decide.
London arbitrators were appointed, but the parties agreed to allow the Commercial Court in London to decide whether or not Thyssen’s claims were time-barred. (English law, like COGSA, includes a one-year time bar on damaged-goods claims.) That court decided that the claims were indeed time-barred and, finding that the delay was Thyssen’s fault and doubting Thyssen’s claims that it had tried and failed to obtain copies of the charter parties, refused to exercise its discretion under the English Arbitration Act to grant an extension. The Commercial Court thereupon dismissed Thyssen’s claims in a decision that Thyssen did not appeal.
The case returned to the federal district court, which confirmed the arbitration award and finally disposed of all of Thys-sen’s claims. In so doing, the court turned aside arguments by Thyssen that (1) the arbitration was aborted and should therefore be voided pursuant to 9 U.S.C. § 10(a)(4), and (2) that since arbitrators have no in rem jurisidiction under English law, any contractual clause purporting to force London arbitration of in rem claims would be void under COGSA, 46 U.S.C. § 1303(8).
Thyssen appeals these two decisions of the district court on four grounds: (1) Calypso waived arbitration by waiting as long as it did before raising its right to arbitrate. (2) Dismissal of Thyssen’s in rem action against the MAREOS N deprived Thyssen of a remedy. (3) Requiring London arbitration of Thyssen’s in rem claims violates COGSA § 3(8).(4) The arbitration clause in the charter party should not be enforced, because neither party to the bill of lading was a signatory of the charter party, and because Thyssen was unaware of the charter party’s contents.
DISCUSSION
I. Waiver
We review de novo a district court’s decision regarding waiver of a party’s right to arbitrate, but we review the factual findings on which the district court relied for clear error. See S & R Co. of Kingston v. Latona Trucking, Inc., 159 F.3d 80, 83 (2d Cir.1998).
“[TJhere is a strong presumption in favor of arbitration^ and] waiver of the right to arbitration is not to be lightly *105inferred.” Coca-Cola Bottling Co. v. Soft Drink and Brewe'ty Workers Union Local 812, 242 F.3d 52, 57 (2d Cir.2001) (internal quotation marks omitted). “An inquiry into whether an arbitration right has been waived is factually specific and not susceptible to bright line rules.” Cotton v. Slone, 4 F.3d 176, 179 (2d Cir.1993). Generally, waiver is more likely to be found the longer the litigation goes on, the more a party avails itself of the opportunity to litigate, and the more that party’s litigation results in prejudice to the opposing party. Leadertex, Inc. v. Morganton Dyeing & Finishing Corp., 67 F.3d 20, 25 (2d Cir.1995).
The key to a waiver analysis is prejudice. “[Wjaiver of the right to compel arbitration due to participation in litigation may be found only when prejudice to the other party is demonstrated.” Rush v. Oppenheimer & Co., 779 F.2d 885, 887 (2d Cir.1985). This Court has recognized two types of prejudice: substantive prejudice and prejudice due to excessive cost and time delay. “Prejudice can be substantive, such as when a party loses a motion on the merits and then attempts, in effect, to relitigate the issue by invoking arbitration, or it can be found when a party too long postpones his invocation of his contractual right to arbitration, and thereby causes his adversary to incur unnecessary delay or expense.” Kramer v. Hammond, 943 F.2d 176, 179 (2d Cir.1991).
In the instant case, it is clear that Thyssen did not face excessive costs. Though there was a significant length of time between the filing of the complaint and the assertion of Calypso’s right to arbitrate, there was no evidence of extensive discovery or substantive motions by Calypso. This Circuit has refused to find waiver in a number of cases where delay in trial proceedings was not accompanied by substantial motion practice or discovery. See, e.g., Shearson Lehman Hutton, Inc. v. Wagoner, 944 F.2d 114, 122 (2d Cir.1991) (holding there was no waiver even though defendant did not raise arbitration after knowing about his rights for three years); see also Thomas v. A.R. Baron & Co., 967 F.Supp. 785, 789 (S.D.N.Y.1997) (no waiver despite a year and a half of delay); Ac-quaire v. Canada Dry Bottling, 906 F.Supp. 819, 830 (E.D.N.Y.1995) (no waiver of arbitration by the defendant where the three-year delay was mostly due to motions presented by the plaintiff). Absent evidence of excessive cost, the presumption in favor of arbitration cannot be overcome merely on the basis of the length of the delay.
In arguing substantive prejudice, Thys-sen offers two theories. First, it contends that Fed.R.Civ.P. 8(c) requires all affirmative defenses, and arbitration in particular, to be pleaded in the answer. Accordingly, Thyssen cites McDonnell v. Dean Witter Reynolds, Inc., 620 F.Supp. 152, 155-56 (D.Conn.1985) (citations omitted): “[U]n-der Fed.R.Civ.P. 8(c), the affirmative defense of arbitration must appear in the answer, and a party’s failure to plead an affirmative defense bars its invocation at later stages of litigation.... [I]f the defense is not set forth in the answer, [the defendant] already waived the right to litigate the issue.”
This argument runs afoul of the applicable precedent of this Court: “Absent a demonstration of prejudice by [the defendant], the bare fact that the defendants filed an answer is inadequate by itself to support a claim of waiver of arbitration.” Rush, 779 F.2d at 889. While not pleading arbitration in the answer can be used as evidence towards finding of waiver, see Com Tech Assocs. v. Computer Assocs. Int’l, Inc., 938 F.2d 1574, 1577 (2d Cir.1991), there is no per se rule that arbitration must be pleaded in the answer in *106order to avoid waiver. Moreover, nothing in the text of Fed. R. Civ. P 8(c) calls the requirement of prejudice into question. Rule 8(c) does require a defendant to set forth any defense of “arbitration and award,” but this is different from a motion to stay pending arbitration. Rather, it refers to a situation in which an arbitrator has already ruled. “Clearly, Rule 8(c) is limited to the situation where a dispute already has been arbitrated and an award has been obtained.” Lee v. Grandcor Med. Sys., Inc., 702 F.Supp. 252, 254 (D.Colo.1988).
Thyssen’s second argument is that it was substantively prejudiced by the fact that its claim was time-barred by the time arbitration was reached. But Calypso correctly responds that the applicable one-year limitation period had effectively expired before the defendant even answered. Thus, there was no substantive prejudice. We therefore agree with the district court’s conclusion that there was no waiver. Cf. e.g., Rush, 779 F.2d at 887 (no waiver where there was “extensive involvement over the course of eight months in the litigation, including taking rather extensive discovery, bringing a motion to dismiss, and posing thirteen affirmative defenses to the amended complaint, all without raising the right to arbitration” but no prejudice was shown).
II. In Rem Claims
Thyssen makes two separate but related arguments regarding the refusal of the district court to entertain its in rem action against the vessel. First, Thyssen claims that its in rem rights, which it maintains are distinct and separable from its in per-sonam rights against Calypso, were not and could not be adjudicated by the London arbitrators and hence should not have been made to depend on that arbitration. Second, Thyssen asserts that under COG-SA § 3(8), 46 U.S.C. § 1303(8), its in rem rights could not properly be submitted to London arbitration.
A. FAA Section 8 Precludes Thys-sen’s In Rem Claim.
Thyssen argues that the district court erred in dismissing its in rem claim because the arbitrator ruled only on the in personam claim. English law does not grant arbitrators in rem jurisdiction, and, Thyssen argues, this means that the dismissal of the in personam claim should have no bearing on its in rem action. Section 8 of The Federal Arbitration Act (“FAA”), however, addresses this concern directly, making clear that where there is an arbitration clause in a contract, in rem proceedings serve to provide a plaintiff with security while the in personam claim awaits arbitration. See 9 U.S.C. § 8. The very applicability of the FAA to maritime contracts rests on this point. Almost all maritime disputes generate both an in personam and an in rem claim; if plaintiffs were able to bring in rem claims in court after the failure of their in personam claims before an arbitrator, parties would have no incentive to arbitrate maritime matters.
The FAA provides that the Act applies to arbitration agreements in maritime transactions, which include “charter parties, bills of lading of water carriers ... collisions, or any other matters in foreign commerce which, if the subject controversy, would be embraced within admiralty jurisdiction.” 9 U.S.C § 1. All of these transactions give rise to in rem claims against ships. Section 8 of the Act explains clearly how such in rem claims must be handled:
If the basis of jurisdiction be a cause of action otherwise justiciable in admiralty, then ... the party claiming to be aggrieved may begin his proceeding here*107under by libel and seizure of the vessel or other property of the other party according to the usual course of admiralty proceedings, and the court shall then have jurisdiction to direct the parties to proceed with the arbitration and shall retain jurisdiction to enter its decree upon the award.
Id. § 8. Under § 8, the plaintiff may seize the ship in rem, obtain a bond, and proceed with arbitration. If the plaintiff wins but cannot recover against the owner of the vessel, it can recover against the vessel itself. See Diana Compania Maritima, S.A. v. The Subfreights of the S.S. Admiralty Flyer, 280 F.Supp. 607, 615 (S.D.N.Y.1968). The in rem claim serves as a way of making sure that a plaintiff can recover if it wins in arbitration. Any interpretation of the FAA that allowed an in rem claim to proceed after the failure of an in personam claim would undermine the purpose of the Act with respect to maritime proceedings. All maritime contracts that called for arbitration of in personam claims could be sidestepped simply by bringing in rem claims. The FAA clearly states that it controls maritime transactions, and we must interpret it in a way that furthers that purpose.2
B. Referral of Thyssen’s In Rem Claim to a London Arbitrator Does Not Violate COGSA § 3(8).
COGSA § 3(8) states that “[a]ny clause, covenant, or agreement in a contract of carriage relieving the carrier of the ship from liability for loss or damage to or in connection with goods, arising from negligence, fault or failure ... shall be null and void and of no effect.” 46 U.S.C. § 1303(8). Thyssen argues that, given the London Arbitrator’s lack of in rem jurisdiction, the arbitration clause in the charter party operated as such a clause, and hence upholding the arbitrator’s decision violates § 1303(8). Even assuming arguendo that the lack of an in rem cause of action could be considered a violation of COGSA (a ruling that would contradict most case law on the matter, see, e.g., Fireman’s Fund Ins. Co. v. M.V. DSR Atlantic, 131 F.3d 1336, 1339-40 (9th Cir.1998)), there was no violation in the instant case, because Thyssen’s in rem rights were protected. Thyssen accepted from the owner of the MAREOS N a Club Letter of Undertaking for $600,000 as full security for its claims. Had it won in arbitration and had the owner of the MAREOS N tried to avoid the court’s order, Thyssen could have recovered against the Club Letter. A letter of undertaking replaces the vessel as the res and moots the question of the need for separate in rem claim. See, e.g., Salim Oleochemicals, Inc. v. M/V Shropshire, 169 F.Supp.2d 194, 200 (S.D.N.Y.2001); Macsteel Int’l USA Corp. v. M/V Spar Two, 2002 WL 472018, 2002 U.S. Dist. LEXIS 5127, at *4 (2002); Reed & Barton Corp. v. M/V Tokio Express, 1999 WL 92608, 1999 U.S. Dist. LEXIS 1807, at *7, (1999). It follows therefore that the district court was correct in its conclusion that § 1303(8) did not render the charter party’s arbitration clause invalid.
III. Applicability of the Arbitration Clause to Non-signatories of the Charter Party Ignorant of the Charter Party’s Contents
Thyssen does not dispute that it can be bound to arbitrate its claims by signing a document that incorporates another document by reference. Rather, it claims it *108had no actual or constructive notice of the terms of the charter party that was incorporated and hence that it could not be deemed to be a signatory of that agreement. For all of the reasons stated by the district court, we agree that the charter party provisions were properly incorporated into the bill of lading and that the charter party bound both Thyssen and Calypso.
CONCLUSION
Having reviewed all of Thyssen’s claims and finding them to be without merit, we AFFIRM the district court’s grant of summary judgment to the Defendant-appel-lees.
. Defendant-appellee A.M. Nomikos & Son Ltd. manages the ship.
. We do not decide today the issue of whether admiralty claims in rem can ever survive the dismissal of in personam claims.