Appeal and cross appeal from an order of the Supreme Court, Erie County (Deborah A. Chimes, J.), entered June 11, 2012 in a proceeding pursuant to CPLR article 75. The order, among other things, dismissed the petition.
It is hereby ordered that said cross appeal is unanimously dismissed and the order is affirmed without costs.
Memorandum: Petitioner commenced this proceeding pursuant to CPLR article 75 seeking a permanent stay of arbitration with respect to a grievance arising from petitioner’s termination of an employee. Petitioner appeals and respondent cross-appeals from an order that, inter alia, dismissed the petition.
*1495Contrary to petitioner’s contention, we conclude that Supreme Court properly dismissed the petition. In determining whether an issue is subject to arbitration under a collective bargaining agreement (CBA), a court must apply the two-step analysis set forth in Matter of Acting Supt. of Schools of Liverpool Cent. School Dist. (United Liverpool Faculty Assn.) (42 NY2d 509, 513 [1977]). “First, a court must determine whether there is any statutory, constitutional or public policy prohibition against arbitration of the grievance” (Matter of Mariano v Town of Orchard Park, 92 AD3d 1232, 1233 [2012] [internal quotation marks omitted]; see Matter of United Fedn. of Teachers, Local 2, AFT, AFL-CIO v Board of Educ. of City School Dist. of City of N.Y., 1 NY3d 72, 79 [2003]). If the court determines that there is no such prohibition and thus that the parties have the authority to arbitrate the grievance, it proceeds to the second step, in which it must determine whether that authority was in fact exercised, i.e., whether the CBA demonstrates that the parties agreed to refer this type of dispute to arbitration (see Acting Supt. of Schools of Liverpool Cent. School Dist., 42 NY2d at 513). With respect to the second step, where there is a broad arbitration clause such as the one in the CBA at issue, “[a] determination of arbitrability is limited to ‘whether there is a reasonable relationship between the subject matter of the dispute and the general subject matter of the CBA’ ” (Matter of Haessig [Oswego City School Dist.], 90 AD3d 1657, 1657 [2011], quoting Matter of Board of Educ. of Watertown City School Dist. [Watertown Educ. Assn.], 93 NY2d 132, 143 [1999]). “Succinctly, the test centers on two distinct inquiries as to the public parties’ purported entry into the arbitral forum: may they do so and, if yes, did they do so” (Board of Educ. of Watertown City School Dist., 93 NY2d at 138). Here, with respect to the issue whether petitioner properly followed the procedures mandated by the CBA in terminating the employee in question, we conclude that the court properly determined that the parties had the authority to agree to arbitrate this grievance, and that they in fact agreed to do so.
Petitioner’s contention that the provisions of the CBA violate public policy and the Civil Service Law, which concerns the first step of the test, is raised for the first time on appeal. We nevertheless review that contention inasmuch as it involves “[a] question of law appearing on the face of the record . . . [that] could not have been avoided by the opposing party if brought to that party’s attention in a timely manner” (Oram v Capone, 206 AD2d 839, 840 [1994]). We reject petitioner’s contention, however, and conclude that Civil Service Law § 75 “may be supplemented, modified or replaced by agreements negotiated *1496between the state and an employee organization pursuant to article fourteen of this chapter” (§ 76 [4]; cf. Matter of City of Long Beach v Civil Serv. Empls. Assn., Inc. — Long Beach Unit, 8 NY3d 465, 470 [2007]).
We reject petitioner’s further contention that strict compliance with the three-step grievance procedure set forth in the CBA is a condition precedent to arbitration. “Questions concerning compliance with a contractual step-by-step grievance process have been recognized as matters of procedural arbitrability to be resolved by the arbitrators, particularly in the absence of a very narrow arbitration clause or a provision expressly making compliance with the time limitations a condition precedent to arbitration” (Matter of Enlarged City School Dist. of Troy [Troy Teachers Assn.], 69 NY2d 905, 907 [1987]; see Matter of Kachris [Sterling], 239 AD2d 887, 888 [1997]).
Finally, we note that respondent cross-appeals from the order “insofar as it held that whether the steps to reach arbitration were complied with [is] for the Court to decide.” The cross appeal must be dismissed. “The fact that the . . . order contains language or reasoning that [respondent] deems adverse to its interests does not furnish a basis for standing to take a[ ] [cross] appeal” (Pramco III, LLC v Partners Trust Bank, 52 AD3d 1224, 1225 [2008] [internal quotation marks omitted]; see Matter of El-Roh Realty Corp., 55 AD3d 1431, 1434 [2008]). Consequently, even assuming, arguendo, that the notice of cross appeal was timely filed (see CPLR 2103 [b] [2]; 5513 [a]; cf. AXA Equit. Life Ins. Co. v Kalina, 101 AD3d 1655, 1657 [2012]), we conclude that respondent is not an aggrieved party (see generally CPLR 5511). Present — Smith, J.P., Fahey, Sconiers, Valentino and Whalen, JJ.