BOGGS, Circuit Judge.
An immigrant, Anna Boar, argues that she has successfully vacated a state conviction, for immigration purposes, when a state court allowed her to withdraw her guilty plea to that conviction and entered a guilty plea nunc pro tunc to a different offense that would have no immigration consequences. We affirm the judgment of the Board of Immigration Appeals (BIA) that she has not done so, because the only reasonable inference that can be drawn from the record is that the vacating court took this action in order to prevent Boar from being deported.
I
Anna Boar is a citizen of Romania who was admitted to the United States in 1995 as an immigrant. On August 24, 1998, when Boar was twenty years old, she was convicted as a Youthful Trainee, as defined in Michigan Complied Laws (M.C.L.) § 762.11,1 for the offense of first-degree [616]*616retail fraud.2 Boar pleaded guilty to this offense. She was sentenced to one year of probation. On August 23, 1999, Boar was discharged from probation and her criminal case was dismissed pursuant to the Youthful Trainee Act.
On December 27, 1999, shortly after the offense was discharged, the former Immigration and Naturalization Service filed a Notice to Appear with the Detroit, Michigan Immigration Court, charging that Boar was removable as an alien convicted of a crime of moral turpitude, committed within five years of admission, for which a sentence of one year or more may be imposed. Immigration and Nationality Act (INA) § 237(a)(2)(A)(i); 8 U.S.C. § 1227(a)(2)(A)(i).
On July 12, 2000 Boar attended a hearing before an immigration judge, where she denied that she had been convicted of first-degree retail fraud, and thus denied that she was removable. She filed a motion on the same day to terminate the removal proceedings, arguing that she had no criminal convictions for purposes of INA § 237(a)(2)(A)(I) because her conviction had been dismissed pursuant to the Youthful Trainee Act.
Boar next sought to vacate the retail-fraud offense from her record entirely. On September 11, 2000, the Circuit Court for Oakland County, Michigan, allowed Boar to withdraw her guilty plea to first-degree retail fraud. The court also allowed Boar to instead enter a plea nunc pro tunc to second-degree retail fraud, in violation of M.C.L. § 750.356d, an offense punishable as “a 93-day misdemeanor.”3 The court did not provide reasoning for its decision. Boar’s motion, however, stated that she had completed her probation; all the defrauded property had been returned; that no damage to the property was suffered; she owed no restitution; that she had been discharged from probation; that she had not been found in violation of any laws since that offense; and that she was a part-time student who worked two jobs to support her family. Boar also handwrote on the typewritten motion that she wished to withdraw her guilty plea “[pjursuant to MCR § 6.500 et seq.”4
On October 12, 2000, Boar filed a renewed motion to terminate the removal [617]*617proceedings in the immigration court. She withdrew her former argument that she had no convictions on her record.5 Instead, she argued that her guilty plea to first-degree retail fraud had been set aside due to an infirmity in the legal proceedings. She did not provide any evidence of a legal infirmity other than the nunc pro tunc plea to second-degree retail fraud.
At a hearing before the immigration court on July 3, 2001, the immigration judge stated that Boar had not met her burden of proof that the Michigan state court’s post-conviction actions eliminated her conviction for immigration purposes. The judge reasoned that the Circuit Court had not indicated the basis for its vacation of her conviction, and that Boar’s argument that the conviction had been vacated due to a legal infirmity could not be proved.
The immigration judge later denied Boar’s withholding of removal and ordered her to be removed to Romania under INA § 237(a)(2)(A)®, 8 U.S.C. § 1227(a)(2)(A)®. The judge denied Boar’s renewed motion to terminate the removal proceedings because Boar did not demonstrate that her conviction was vacated for constitutional or statutory purposes as opposed to for rehabilitative purposes.
Boar appealed the decision. She argued that the immigration judge erred in holding that her conviction made her subject to removal, because her new conviction, entered nunc pro tunc by the Circuit Court, carried a maximum penalty of only 93 days and therefore did not qualify as an offense that permits removal under INA § 237(a)(2)(A)®, 8 U.S.C. § 1227(a)(2)(A)®.
The BIA dismissed Boar’s appeal, adopting and affirming the immigration judge’s decision. The BIA determined that the Circuit Court had changed Boar’s plea nunc pro tunc to “enhance her immigration status” and that Boar “remain[ed] convicted for immigration purposes of the initial crime involving moral turpitude.”
On February 7, 2006, Boar filed a petition for review of the Board’s decision. On January 8, 2007, the Attorney General filed an unopposed motion to remand the proceedings in light of Pickering v. Gonzales, 465 F.3d 263 (6th Cir.2006), which changed the burden of proof in cases like Boar’s, holding that the Department of Homeland Security (DHS) had the burden of showing by clear and convincing evidence that the petitioner’s conviction was vacated solely for rehabilitative or immigration purposes.
On March 13, 2007, the Sixth Circuit granted this motion, citing Pickering and Sanusi v. Gonzales, 474 F.3d 341 (6th Cir.2007), a case in which the government had been successful in meeting this new burden. The Board of Immigration Appeals then remanded the case to the immigration judge to permit the parties to present argument and evidence on whether the DHS had met its burden of proof. The Board also ordered the immigration judge to address Boar’s removability under Matter of Cota-Vargas, 23 I. & N. Dec. 849 (BIA 2005), which held that a trial court’s decision to modify or reduce an alien’s sentence nunc pro tunc is entitled to full faith and credit, and that the modification or reduction is valid for purposes of the immigration law without regard to the court’s reasoning for its decision.
[618]*618On remand, the immigration judge denied Boar’s motion to terminate the removal proceedings. The judge found that the Circuit Court’s decision to withdraw Boar’s guilty plea to first-degree retail fraud was in fact based on Boar’s successful rehabilitation after the offense.- The judge determined that the transcript of the hearing in front of the Circuit Judge “clearly indicate[d] that [Boar’s] withdrawal of her initial plea and the subsequent nunc pro tunc plea was entered based on Boar’s rehabilitation.” The immigration judge again ordered that Boar be removed to Romania.
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BOGGS, Circuit Judge.
An immigrant, Anna Boar, argues that she has successfully vacated a state conviction, for immigration purposes, when a state court allowed her to withdraw her guilty plea to that conviction and entered a guilty plea nunc pro tunc to a different offense that would have no immigration consequences. We affirm the judgment of the Board of Immigration Appeals (BIA) that she has not done so, because the only reasonable inference that can be drawn from the record is that the vacating court took this action in order to prevent Boar from being deported.
I
Anna Boar is a citizen of Romania who was admitted to the United States in 1995 as an immigrant. On August 24, 1998, when Boar was twenty years old, she was convicted as a Youthful Trainee, as defined in Michigan Complied Laws (M.C.L.) § 762.11,1 for the offense of first-degree [616]*616retail fraud.2 Boar pleaded guilty to this offense. She was sentenced to one year of probation. On August 23, 1999, Boar was discharged from probation and her criminal case was dismissed pursuant to the Youthful Trainee Act.
On December 27, 1999, shortly after the offense was discharged, the former Immigration and Naturalization Service filed a Notice to Appear with the Detroit, Michigan Immigration Court, charging that Boar was removable as an alien convicted of a crime of moral turpitude, committed within five years of admission, for which a sentence of one year or more may be imposed. Immigration and Nationality Act (INA) § 237(a)(2)(A)(i); 8 U.S.C. § 1227(a)(2)(A)(i).
On July 12, 2000 Boar attended a hearing before an immigration judge, where she denied that she had been convicted of first-degree retail fraud, and thus denied that she was removable. She filed a motion on the same day to terminate the removal proceedings, arguing that she had no criminal convictions for purposes of INA § 237(a)(2)(A)(I) because her conviction had been dismissed pursuant to the Youthful Trainee Act.
Boar next sought to vacate the retail-fraud offense from her record entirely. On September 11, 2000, the Circuit Court for Oakland County, Michigan, allowed Boar to withdraw her guilty plea to first-degree retail fraud. The court also allowed Boar to instead enter a plea nunc pro tunc to second-degree retail fraud, in violation of M.C.L. § 750.356d, an offense punishable as “a 93-day misdemeanor.”3 The court did not provide reasoning for its decision. Boar’s motion, however, stated that she had completed her probation; all the defrauded property had been returned; that no damage to the property was suffered; she owed no restitution; that she had been discharged from probation; that she had not been found in violation of any laws since that offense; and that she was a part-time student who worked two jobs to support her family. Boar also handwrote on the typewritten motion that she wished to withdraw her guilty plea “[pjursuant to MCR § 6.500 et seq.”4
On October 12, 2000, Boar filed a renewed motion to terminate the removal [617]*617proceedings in the immigration court. She withdrew her former argument that she had no convictions on her record.5 Instead, she argued that her guilty plea to first-degree retail fraud had been set aside due to an infirmity in the legal proceedings. She did not provide any evidence of a legal infirmity other than the nunc pro tunc plea to second-degree retail fraud.
At a hearing before the immigration court on July 3, 2001, the immigration judge stated that Boar had not met her burden of proof that the Michigan state court’s post-conviction actions eliminated her conviction for immigration purposes. The judge reasoned that the Circuit Court had not indicated the basis for its vacation of her conviction, and that Boar’s argument that the conviction had been vacated due to a legal infirmity could not be proved.
The immigration judge later denied Boar’s withholding of removal and ordered her to be removed to Romania under INA § 237(a)(2)(A)®, 8 U.S.C. § 1227(a)(2)(A)®. The judge denied Boar’s renewed motion to terminate the removal proceedings because Boar did not demonstrate that her conviction was vacated for constitutional or statutory purposes as opposed to for rehabilitative purposes.
Boar appealed the decision. She argued that the immigration judge erred in holding that her conviction made her subject to removal, because her new conviction, entered nunc pro tunc by the Circuit Court, carried a maximum penalty of only 93 days and therefore did not qualify as an offense that permits removal under INA § 237(a)(2)(A)®, 8 U.S.C. § 1227(a)(2)(A)®.
The BIA dismissed Boar’s appeal, adopting and affirming the immigration judge’s decision. The BIA determined that the Circuit Court had changed Boar’s plea nunc pro tunc to “enhance her immigration status” and that Boar “remain[ed] convicted for immigration purposes of the initial crime involving moral turpitude.”
On February 7, 2006, Boar filed a petition for review of the Board’s decision. On January 8, 2007, the Attorney General filed an unopposed motion to remand the proceedings in light of Pickering v. Gonzales, 465 F.3d 263 (6th Cir.2006), which changed the burden of proof in cases like Boar’s, holding that the Department of Homeland Security (DHS) had the burden of showing by clear and convincing evidence that the petitioner’s conviction was vacated solely for rehabilitative or immigration purposes.
On March 13, 2007, the Sixth Circuit granted this motion, citing Pickering and Sanusi v. Gonzales, 474 F.3d 341 (6th Cir.2007), a case in which the government had been successful in meeting this new burden. The Board of Immigration Appeals then remanded the case to the immigration judge to permit the parties to present argument and evidence on whether the DHS had met its burden of proof. The Board also ordered the immigration judge to address Boar’s removability under Matter of Cota-Vargas, 23 I. & N. Dec. 849 (BIA 2005), which held that a trial court’s decision to modify or reduce an alien’s sentence nunc pro tunc is entitled to full faith and credit, and that the modification or reduction is valid for purposes of the immigration law without regard to the court’s reasoning for its decision.
[618]*618On remand, the immigration judge denied Boar’s motion to terminate the removal proceedings. The judge found that the Circuit Court’s decision to withdraw Boar’s guilty plea to first-degree retail fraud was in fact based on Boar’s successful rehabilitation after the offense.- The judge determined that the transcript of the hearing in front of the Circuit Judge “clearly indicate[d] that [Boar’s] withdrawal of her initial plea and the subsequent nunc pro tunc plea was entered based on Boar’s rehabilitation.” The immigration judge again ordered that Boar be removed to Romania.
Boar appealed the immigration judge’s decision to the BIA. The BIA dismissed the appeal, holding that the DHS had proven that Boar’s motion to withdraw her guilty plea to first-degree retail fraud was based on rehabilitation and immigration purposes. The BIA determined that Matter of Cotar-Vargas was inapposite because Boar’s case involved the vacatur of her conviction, not just the modification or reduction of her sentence.
Boar has appealed the BIA’s decision. We deny the petition for review.
II
Boar raises three issues in her appeal, but these collapse into one. Boar contends that her motion to terminate the removal proceedings should have been granted based on the withdrawal of her guilty plea and her subsequent nunc pro tunc plea to second-degree retail fraud, because the nunc pro tunc plea to second-degree retail fraud completely eliminated her earlier conviction for first-degree retail fraud. She argues that Matter of Cota-Vargas required the immigration judge to give the nunc pro tunc plea full faith and credit with no regard to the reasons the judge gave for making it.
Where the BIA adopts an immigration judge’s reasoning while adding its own comments, as is the case here, this court reviews both the immigration judge’s and the BIA’s decision. Singh v. Ashcroft, 398 F.3d 396, 400-01 (6th Cir.2005). On petitions from BIA decisions, we review questions of law de novo, but give “substantial deference” to the BIA’s interpretation of the INA. Ikharo v. Holder, 614 F.3d 622, 629 (6th Cir.2010) (internal quotation marks omitted). Whether an alien’s conviction renders her removable is a legal question that we review de novo. Sanusi, 474 F.3d at 345 (internal quotation marks omitted).
For immigration purposes, a conviction is:
[A] formal judgment of guilty of the alien entered by a court or, if adjudication of guilt has been withheld, where— (i) a judge or jury has found the alien guilty or the alien has entered a plea of guilty or nolo contendré or has admitted sufficient facts to warrant a finding of guilt, and (ii) the judge has ordered some form of punishment, penalty, or restraint on the alien’s liberty to be imposed.
INA § 101(a)(48)(A), 8 U.S.C. § 1101(a)(48)(A) (emphasis added). Vaca-tur of a conviction may render it invalid for immigration purposes, but this depends on the basis of the vacatur. If a conviction is vacated because the process by which it was obtained was defective or illegal, then the conviction is no longer valid for immigration purposes. See Pickering, 465 F.3d at 266 (stating that a conviction vacated “because of procedural or substantive infirmities” is not valid for immigration purposes).
However, if the vacatur was entered for rehabilitative purposes, “solely to avoid immigration hardship,” then the conviction remains valid for immigration purposes. [619]*619Sanusi, 474 F.3d at 345 (citing Pickering, 465 F.3d at 266). The government bears the burden of proof of showing by clear and convincing evidence, either by direct evidence or evidence “from which one could infer and conclude,” that the original court vacated the conviction solely for rehabilitative purposes. Al-Najar v. Mukasey, 515 F.3d 708, 715-16 (6th Cir.2008) (citing Pickering, 465 F.3d at 270). When a court vacates a conviction without explanation, the government may meet its burden when the “alien’s request for vacatur before the state court contained no legal basis to set aside his conviction” because there is no evidence from which to infer that the writ was granted on a recognized legal ground. Al-Najar, 515 F.3d at 717 (citing Sanusi, 474 F.3d at 341).
A conviction for first-degree retail fraud, Boar’s original conviction, is a conviction that permits removal because it is punishable under M.C.L. § 750.356C by imprisonment of up to two years. However, the conviction was vacated by the Circuit Court, and a conviction for second-degree retail fraud, an offense that does not qualify as removable, was entered nunc pro tunc. Therefore, Boar does not have a removable offense on her record, unless the government can show by clear and convincing evidence that the Circuit Court vacated Boar’s guilty plea to first-degree retail fraud solely for rehabilitative or immigration purposes. If it did, then Boar’s conviction for first-degree retail fraud is still valid for immigration purposes, and she is still removable. Al-Najar, 515 F.3d at 715-16.
Boar’s motion in the Circuit Court, on the basis of which it vacated her conviction, provided no justification for vacating the conviction other than a rehabilitative purpose. The only law Boar cited was MCR § 6.500 et seq. Most of chapter 6.500 deals with the process and form to follow when seeking post-appeal relief; it does not provide grounds on which relief can be granted. Subsection 6.508(d)(3), which Boar’s brief suggests applies in her case, states that a court may not grant relief to a defendant if they “allege[] grounds for relief, other than jurisdictional defects, which could have been raised on appeal ... unless the defendant demonstrates ... good cause for failure to raise such grounds on appeal ... and ... actual prejudice [such as] ... in a conviction entered on a plea of guilty, ... the defect in the proceedings was such that it renders the plea an involuntary one.”
Though Boar has indicated that law exists within Chapter 6.500 that could explain why the Circuit Court did not reject post-appeal relief, she still gives no legal basis on which the court could have granted relief. Specifically, her motion failed to discuss any grounds for relief, any “good cause” for not raising these “grounds” on appeal, or any reason why her original plea should have been found involuntary. Her barely articulated reference to law, undeveloped and unsubstantiated, is no better than no reference to law at all. There is no evidence that the Circuit Court could have vacated Boar’s conviction for first-degree retail fraud based on MCR § 6.500 et seq.
Boar’s case is like Sanusi. In Sanusi, the defendant had a conviction for property theft that made him removable for immigration purposes. Sanusi, 474 F.3d at 343. Another court vacated this conviction, without any explanation of its reasoning. Ibid. Because Sanusi had not raised or argued “any colorable legal basis for the vacation of his conviction,” but had only discussed in his motion the “harsh immigration consequences” that the conviction would cause, the Sixth Circuit determined that the only reasonable inference that could be drawn was that the conviction [620]*620was vacated to prevent Sanusi’s deportation. The record here is basically the same.6 The only reasonable inference that can be drawn from the Circuit Court’s decision is that Boar’s guilty plea was withdrawn and her plea to second-degree retail fraud was entered in order to prevent her from being deported. Therefore, the BIA did not err in holding that Boar’s conviction for first-degree retail fraud was still valid for immigration purposes.
We also distinguish this case from Cota-Vargas, 23 I. & N. Dec. 849. Cota-Vargas dealt with sentence modification or reduction, not the vacatur of a conviction. Id. at 850. The question of whether a “conviction” exists under 8 U.S.C. § 1101(a)(48)(A) is separate from the determination of the length of a sentence, or “term of imprisonment,” under 8 U.S.C. § 1101(a)(48)(B). A “state court expungement of a conviction is qualitatively different from a state court order to classify an offense or modify a sentence.” Rumierz v. Gonzales, 456 F.3d 31, 41 n. 11 (1st Cir.2006) (internal quotation marks omitted). Cotar-Vargas itself recognized the distinction in distinguishing the Pickering line of cases, which apply to Boar’s case. Cota-Vargas, 23 I. & N. Dec. at 851-52.
Ill
For the reasons given above, the petition for review of the judgment of the Board of Immigration Appeals is DENIED.