Richard Allen Moore, Texas prisoner # 738493, appeals the district court’s order denying his 28 U.S.C. § 2254 habeas corpus petition, in which he challenged his 1995 jury-trial conviction of aggravated sexual assault and his 25-year prison sentence. This court granted Moore a COA on the issue of whether his trial counsel had performed ineffectively by failing to use Child Protective Services (“CPS”) records to impeach the complainant’s testimony and to support testimony by the complainant’s mother.
Federal habeas relief may not be granted upon any claim that was “adjudicated on the merits in State court” unless the adjudication “resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1). See Williams v. Taylor, 529 U.S. 362, 409, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000).
The trial evidence showed that Moore lived with the mother of the then-nine-year-old complainant and the mother’s other children in various motel rooms. The complainant testified that, on at least one occasion while her mother was out, Moore sexually assaulted her. She did not tell her mother about the assault, but did tell her grandmother, who reported the incident to CPS. A medical examination of the complainant showed that her hymenal membrane had suffered blunt penetrating trauma consistent with sexual intercourse. The complainant’s mother testified that during a visit with the complainant while the latter was in CPS custody, the complainant recanted her accusation against Moore and instead accused the mother’s brother, the complainant’s uncle. When the mother next visited the complainant, she brought a tape recorder and recorded the complainant stating that she had lied about Moore sexually assaulting her and that it was actually her uncle who had raped her. The complainant, however, testified at trial that she had lied on the tape at the insistence of her mother, that *538her uncle had not molested her, and that Moore had. Moore himself testified that he did not assault the complainant.
Moore asserts that the CPS records would have offered additional proof that the complainant was lying when she accused him, that she had made an additional recantation prior to the tape-recorded one addressed at trial, that she had been “coached” by CPS workers to accuse him, and that the complainant’s grandmother was trying to protect the complainant’s uncle. He maintains that the records contained additional instances in which the complainant accused her uncle of the assault. Moore also argues that the CPS records would have shown that he had a “very caring and responsible relationship” with the complainant.
Moore has failed to demonstrate that his counsel’s failure to present CPS records constituted deficient performance or that he was prejudiced by such failure. See Strickland v. Washington, 466 U.S. 668, 689-94, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Contrary to Moore’s assertions, a review of the CPS records does not reflect that they contain strong or substantial proof that the complainant had previously recanted, that she had been coached by CPS workers, or that her grandmother was trying to protect her own son. The CPS records do not reflect that the complainant ever accused her uncle instead of Moore, but only in addition to Moore. At best, the information in the CPS records was cumulative. See Brogdon v. Block-bum, 790 F.2d 1164, 1168-69 (5th Cir. 1986).
The CPS records also contained voluminous evidence of Moore’s bad acts with respect to the complainant, her brother, and her mother. Although an attorney possibly could have had such extraneous evidence excluded under Tex.R. Evid. 404(b) as inadmissible character evidence, some of the evidence could have been admissible to prove identity by rebutting Moore’s defensive theory that someone else, the uncle, committed the assaults. See Johnston v. State, 145 S.W.3d 215, 220 (Tex.Crim.App.2004). Moreover, Moore testified in his own defense at trial. Generally, when a defendant takes the stand, “he is subject to the same rules as any other witness in that he may be impeached, contradicted and cross-examined as to new matters.” Sanchez v. State, 707 S.W.2d 575, 577 (Tex.Crim.App.1986). To the extent that Moore argues that his attorney should have offered the CPS records to reflect his good relationship with and conduct toward the complainant, he would have opened the door for the State to produce rebuttal evidence. See Daggett v. State, 187 S.W.3d 444, 452 (Tex.Crim. App.2005). Moore has not overcome the presumption that his attorneys’ failure to present the CPS records was “sound trial strategy.” See Strickland, 466 U.S. at 689, 104 S.Ct. 2052 (internal quotation omitted). Furthermore, he has failed to show that, in denying relief, the state court acted contrary to or unreasonably applied Supreme Court precedent. Accordingly, we AFFIRM the district court’s denial of habeas relief and reject Moore’s contentions that the court erred in denying his motions for discovery and for an evidentiary hearing. Additionally, Moore’s “Motion for Enlargement to Include New Evidence” is DENIED.
The respondent argues, as an alternative matter, that the district court erred in denying his initial motion for summary judgment, wherein he had argued that Moore’s § 2254 petition was barred by the one-year limitations provision of 28 U.S.C. § 2244(d). Contrary to Moore’s contention, the respondent was not required to file a cross-appeal to raise the limitations argument. See El Paso Natural Gas Co. *539v. Neztsosie, 526 U.S. 473, 479, 119 S.Ct. 1430, 143 L.Ed.2d 635 (1999); Neverson v. Farquharson, 366 F.3d 32, 39 (1st Cir. 2004). Although the Texas Court of Criminal Appeals failed for six months to notify Moore of the rejection of his pro se motion for rehearing of the refusal of his petition for discretionary review, the one-year period did not begin, as Moore argues, on the date Moore received notice. See Crutcher v. Cockrell, 301 F.3d 656, 657 (5th Cir. 2002) (“28 U.S.C. § 2244(d)(1)(A) looks to when a judgment becomes final, not when petitioner becomes aware that the judgment is final.”). Although the six-month delay was sufficient to trigger an analysis of whether Moore was entitled to equitable tolling of the limitations provision, see Phillips v. Donnelly, 216 F.3d 508, 510-11 (5th Cir.), modified on reh’g, 223 F.3d 797 (5th Cir.2000), equitable tolling was not warranted because Moore failed to act with diligence in pursuing state postconviction relief. See Melancon v. Kaylo, 259 F.3d 401, 407-08 (5th Cir.2001). Accordingly, as an alternative ground of denying habeas relief, we hold that the district court erred in failing to dismiss Moore’s petition as time-barred.