Petitioner, who was convicted of aggravated murder (among other offenses) and sentenced to death, appeals from a judgment dismissing his latest petition for post-conviction relief on the ground that it was untimely and improperly successive, contrary to both ORS 138.510(3), which requires a post-conviction petition to be filed within two years of the completion of the direct appeal process, and ORS 138.550, which requires all grounds for relief to be asserted in a petitioner’s first post-conviction proceeding.1 Petitioner acknowledges that his petition is untimely and successive. He argues, however, that he has alleged sufficient facts in the petition to entitle him to invoke the “escape clauses” of ORS 138.510(3) and ORS 138.550(3).2 Those *116escape clauses permit a post-conviction petitioner to seek post-conviction relief outside the limitations period, or in an otherwise successive petition, if those grounds for relief “could not reasonably have been raised” within the two-year limitations period or in the petitioner’s previous petition. ORS 138.510(3); ORS 138.550(3). In response, defendant, the Superintendent of the Oregon State Penitentiary (the superintendent) contends that the judgment dismissing the petition is not appealable. Alternatively, the superintendent urges us to affirm. We conclude that the judgment dismissing the petition is appealable, and, on review for legal error, conclude further that the post-conviction court correctly dismissed the petition as untimely and successive.

APPEALABILITY

We first address the superintendent’s argument that the judgment on review is not appealable. That argument is predicated on ORS 138.525, which provides that “a judgment dismissing a meritless petition is not appealable.” ORS 138.525(3). Under the statute, a “meritless petition” is “one that, when liberally construed, fails to state a claim upon which post-conviction relief may be granted.” ORS 138.525(2); Young v. Hill, 347 Or 165, 173-74, 218 P3d 125 (2009) (construing ORS 138.525 to mean that “no appeal lies from any judgment dismissing a petition for post-conviction relief for failure to state a claim”). The superintendent points to the fact that the post-conviction court’s order of dismissal states that the petition is meritless and argues that we must accept that statement and dismiss the appeal.

We reject the superintendent’s argument. First, although the post-conviction court’s order of dismissal characterized the petition as meritless, the court’s judgment of dismissal did not. Thus, on its face, the judgment is not “a judgment dismissing a meritless petition.” ORS 138.525. And, to the extent the face of the judgment is not dispositive on that point, a review of the record confirms that the trial court did not dismiss the petition as “meritless” as that term is defined in ORS 138.525. The Supreme Court has distinguished between the dismissal of a petition as time-barred and successive and the dismissal of a petition for failure to state a claim, Delzell v. Coursey, 354 Or 597, 318 P3d 749 *117(2013), as have we, Breece v. Amsberry, 279 Or App 648, 650-51, 381 P3d 1086 (2016). Under ORS 138.525, only the latter type of judgment is considered a dismissal of a petition as meritless and therefore not appealable. ORS 138.525; Breece, 279 Or App at 649-50.

Here, the post-conviction court’s order reveals that it dismissed the petition because it concluded that all grounds for relief were untimely and successive. Under Delzell and Breece, that is not a dismissal for failure to state a claim. Although the court also concluded that the allegations in the fourth ground for relief did not state a claim, that determination was not the basis for its dismissal of the petition as whole; it was simply an alternative ground for dismissing a single alleged ground for relief.3 Nothing in ORS 138.525 suggests that the legislature intended that a judgment dismissing a post-conviction petition would not be appealable simply because some subset of the alleged grounds for relief was determined not to state claims. The plain terms of the statute make it applicable only when a post-conviction court determines “the petition” — which we understand to mean the whole petition — is “one that, when liberally construed, fails to state a claim upon which post-conviction relief may be granted.” The post-conviction court did not make that determination here. Consequently, ORS 138.525 does not bar this appeal.

DISMISSAL

The next question is whether the post-conviction court properly dismissed the petition. Because, as petitioner acknowledges, the petition was untimely and successive on its face, to withstand a motion to dismiss, petitioner was required to allege facts that, if proven, would show that he was entitled to avail himself of the escape clauses of ORS 138.510(3) and ORS 138.550(3). As we have explained, “[a]n untimely petition must allege facts that, if supported by evidence, would establish that the grounds for relief could not reasonably have been raised timely.” Morrow v. Maass, 109 Or App 694, 695, 820 P2d 1374 (1991), rev den, 312 Or 676 (1992). The same is true for a successive petition. That *118is, a successive petition must allege facts that, if supported by evidence, would establish that the grounds for relief could not reasonably have been raised in the petitioner’s first post-conviction proceeding. See Cain v. Gladden, 247 Or 462, 464, 430 P2d 1015 (1967) (discussing what a post-conviction petitioner must allege to invoke an escape clause under ORS 138.550); see also Eklof v. Steward, 273 Or App 789, 794 n 4, 359 P3d 570 (2015), rev allowed, 359 Or 525 (2016) (examining Cain and explaining that, although Cain addressed the ORS 138.550(2) escape clause, under Verduzco v. State of Oregon, 357 Or 553, 566, 355 P3d 902 (2015), it was appropriate to look to Cain in construing the ORS 138.550(3) escape clause). In particular, under the Oregon Rules of Civil Procedure, which apply to post-conviction proceedings unless the post-conviction statutes provide otherwise, a petitioner must plead specific facts which, if proved, would show that petitioner’s untimely, successive filing is excused by the escape clauses of ORS 138.510(3) and ORS 138.550(3). Young, 347 Or at 170-71 (Oregon Rules of Civil Procedure generally govern in post-conviction proceedings and, in particular, require a petitioner to plead with factual specificity); see also Holger v. Irish, 316 Or 402, 406-07, 851 P2d 1122 (1993) (interpreting ORCP 18 to require the pleading of specific facts in support of claimed right to recovery). The facts must be alleged in the petition, and may not be supplied by “unsworn statements of counsel” in arguments. Morrow, 109 Or App at 695.

Here, as to the first three alleged grounds for relief, although petitioner’s arguments in his brief posit some reasons why defendant could not have raised them in a timely first petition, the operative petition alleges no specific facts that would permit a finding that the grounds for relief could not reasonably have been raised in a timely manner in petitioner’s previously filed petition. Instead, the petition alleges the broad legal conclusion that “this successive petition is proper because grounds are asserted which could not reasonably have been raised in the initial petition,” without providing any factual specifics as to why that is the case. For that reason, the post-conviction court correctly concluded that the first three alleged grounds for relief were subject to dismissal as untimely and successive. See Morrow, 109 Or App at 695 (affirming dismissal of post-conviction petition *119that was untimely on its face where petition did not allege facts that, if proved, would entitle him to invoke the escape clause of ORS 138.510).

As to the fourth ground for relief, dismissal also was proper, albeit for different reasons. The fourth ground for relief alleges that defendant was denied the effective assistance of post-conviction counsel, a claim that defendant contends is supported by Martinez v. Ryan, 566 US 1, 132 S Ct 309, 182 L Ed 2d 272 (2012). It is unclear to us whether defendant is alleging that any ineffective assistance of post-conviction counsel supplies a basis for relief from his conviction, or if, instead, defendant is contending that his post-conviction counsel’s alleged ineffectiveness provides a basis for him to invoke the escape clauses of ORS 138.510(3) and ORS 138.550(3).

If the former, the allegations in that ground for relief are sufficient to establish that it could not reasonably have been raised in a timely or original petition; such a claim would not accrue until the completion of petitioner’s post-conviction proceedings. Nonetheless, the claim is foreclosed by our decision in Cunningham v. Premo, 278 Or App 106, 123-24, 373 P3d 1167 (2016), and, thus, the post-conviction court properly dismissed it. In Cunningham, we held that “the adequacy of post-conviction counsel cannot be challenged in a later post-conviction proceeding.” Id. at 124 (citation omitted).

If, instead, petitioner intends the allegations in the fourth ground for relief to supply a basis for invoking the escape clause as to the first three grounds for relief, Cunningham forecloses that pathway as well. There, we also held that we “decline to extend the Supreme Court’s rationale in Martinez to post-conviction claims that are barred as successive, and conclude that [a] petitioner may not avail himself of the escape clause based on his claim that former post-conviction counsel was inadequate.” Id. at 124-25. Although Cunningham involved the escape clause under ORS 138.550(3) only, its holding applies with equal force to the escape clause of ORS 138.510(3).

Affirmed.