Judge ERDMANN
delivered the opinion of the court.
Airman First Class (A1C) Michael Tunstall was charged with two specifications of aggravated sexual assault and one specification each of adultery and false official statement, in violation of Articles 120, 134, and 107, Uniform Code of Military Justice (UCMJ), 10 U.S.C. §§ 920, 934, 907 (2006). He pled not guilty to all charges and at a general court-martial with members was convicted of one specification of aggravated sexual assault and the adultery specification. He was found not guilty of the false official statement specification and the remaining specification of aggravated sexual assault, but as to the latter, was found guilty of the lesser included offense of indecent acts. He was sentenced to a bad-conduct discharge, confinement for six months, a reprimand, and reduction to E-l. The convening authority approved the adjudged sentence. The United States Air Force Court of Criminal Appeals (CCA) affirmed the findings and the sentence. United States v. Tunstall, No. ACM 37592, slip op. at 12, 2012 WL 1058996 (A.F.Ct.Crim.App. Mar. 28, 2012).
“[A] military judge can only instruct on a lesser included offense where the greater offense requires members to find a disputed factual element which is not required for conviction of the lesser violation.” United States v. Miergrimado, 66 M.J. 34, 36 (C.A.A.F.2008). In addition, “[t]he due process principle of fair notice mandates that ‘an accused has a right to know what offense and under what legal theory’ he will be convicted.” United States v. Jones, 68 M.J. 465, 468 (C.A.A.F.2010) (citing United States v. Medina, 66 M.J. 21, 26-27 (C.A.A.F.2008)). “[T]he Due Process Clause of the Fifth Amendment also does not permit convicting an accused of an offense with which he has not been charged.” United States v. Girouard, 70 M.J. 5, 10 (C.A.A.F.2011).
We granted review to determine whether the offense of indecent acts was a lesser included offense of aggravated sexual assault. We conclude that, as charged in this case, indecent acts (committing a sexual act in an open and notorious manner) is not a lesser included offense of aggravated sexual assault (engaging in a sexual act with an incapacitated person). It was therefore error for the military judge to instruct on indecent acts.
We also granted an issue as to whether the adultery specification charged under Article 134 failed to state an offense because it did [193]*193not expressly allege the terminal element.1 We conclude that the record of trial demonstrates that Tunstall was on actual notice of the terminal element and therefore that he was not prejudiced by its omission. See United States v. Humphries, 71 M.J. 209 (C.A.A.F.2012).
Background
In April of 2009, Tunstall and Airman KAS, who were assigned to Hurlburt Field, Florida, were with a group of airmen who spent the day drinking at the beach and in an Air Force dormitory. The two were flirting throughout the afternoon and later were involved in a drinking game with two other airmen in the dorm. The airmen became drunk and during the drinking game KAS removed her clothes and straddled Tunstall, who began to digitally penetrate her vagina in the presence of the two other airmen. The Government considered this episode of sexual activity to be consensual. Shortly thereafter, however, KAS fell to the floor and began to vomit. At this point KAS was described as conscious but not vocal or making any actions. Tunstall and another airman helped KAS to a sink where she continued to have the dry heaves. While KAS was leaning over the sink Tunstall digitally penetrated her vagina until the other airman said, “[i]t’s not time for that. I mean she’s sick. We need to take care of her.” Tun-stall and another airman then helped KAS to the bathroom. During this period KAS was described as definitely intoxicated and rolling in and out of consciousness. Tunstall then locked himself in the bathroom with KAS and had sexual intercourse with her in the shower.2
Specification 2 of Charge I charged Tun-stall with aggravated sexual assault under Article 120 for the digital penetration of KAS’s vagina while she was leaning over the sink and while she was substantially incapable of declining participation. During his instructions on findings, the military judge sua sponte instructed the members that the offense of indecent acts was a lesser included offense of the charged offense of aggravated sexual assault. Tunstall was acquitted of aggravated sexual assault under Specification 2 of Charge I, but was found guilty of the lesser included offense of indecent acts.
Tunstall did not object to the instruction at trial, but on appeal to the CCA he argued that the military judge erred in giving a lesser included offense instruction for the offense of indecent acts. Tunstall, No. ACM 37592, slip op. at 7-11. The CCA held that the offense of indecent acts was a lesser included offense of aggravated sexual assault. Id. at 11. Although the lower court did not conduct an element-by-element comparison of the charges, it concluded that “one cannot engage in a ‘sexual act’ with someone who was vomiting in a sink in the presence of a third party without also engaging in an indecent act.” Id. at 10.
Issue I
Lesser Included Offense
Whether an offense is a lesser included offense is a question of law that is reviewed de novo. United States v. Girouard, 70 M.J. 5, 9 (C.A.A.F.2011). While the granted issue frames our analysis in terms of a lesser included offense, we believe that this ease raises important instructional and notice issues as well.
Because there was no objection to the instruction at trial, we review for plain error. United States v. Wilkins, 71 M.J. 410, 412 (C.A.A.F.2012) (citing United States v. Arriaga, 70 M.J. 51, 54 (C.A.A.F.2011)). Under a plain error analysis, the accused “has [194]*194the burden of demonstrating that: (1) there was error; (2) the error was plain or obvious; and (3) the error materially prejudiced a substantial right of the accused.” Girouard, 70 M.J. at 11.
This court applies the elements test to determine whether one offense is a lesser included offense of another. United States v. Jones, 68 M.J. 465, 468 (C.A.A.F.2010).
Under the elements test, one compares the elements of each offense. If all of the elements of offense X are also elements of offense Y, then X is an LIO of Y. Offense Y is called the greater Offense because it contains all of the elements of offense X along with one or more additional elements.
Id. at 470.
The elements of aggravated sexual assault under Article 120, as charged in this case, are: (1) that the accused engaged in a sexual act with another person; and (2) the other person was substantially incapable of declining participation in the sexual act. Manual for Courts-Martial, United States pt. IV, para. 45.b.(3)(c) (2008 ed.) (MCM). Specification 2 of Charge I alleged that Tun-stall:
did ... engage in a sexual act, to wit: digital penetration by [Tunstall] of the vagina, with [A1C KAS], who was substantially incapable of declining participation in the sexual act.
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Judge ERDMANN
delivered the opinion of the court.
Airman First Class (A1C) Michael Tunstall was charged with two specifications of aggravated sexual assault and one specification each of adultery and false official statement, in violation of Articles 120, 134, and 107, Uniform Code of Military Justice (UCMJ), 10 U.S.C. §§ 920, 934, 907 (2006). He pled not guilty to all charges and at a general court-martial with members was convicted of one specification of aggravated sexual assault and the adultery specification. He was found not guilty of the false official statement specification and the remaining specification of aggravated sexual assault, but as to the latter, was found guilty of the lesser included offense of indecent acts. He was sentenced to a bad-conduct discharge, confinement for six months, a reprimand, and reduction to E-l. The convening authority approved the adjudged sentence. The United States Air Force Court of Criminal Appeals (CCA) affirmed the findings and the sentence. United States v. Tunstall, No. ACM 37592, slip op. at 12, 2012 WL 1058996 (A.F.Ct.Crim.App. Mar. 28, 2012).
“[A] military judge can only instruct on a lesser included offense where the greater offense requires members to find a disputed factual element which is not required for conviction of the lesser violation.” United States v. Miergrimado, 66 M.J. 34, 36 (C.A.A.F.2008). In addition, “[t]he due process principle of fair notice mandates that ‘an accused has a right to know what offense and under what legal theory’ he will be convicted.” United States v. Jones, 68 M.J. 465, 468 (C.A.A.F.2010) (citing United States v. Medina, 66 M.J. 21, 26-27 (C.A.A.F.2008)). “[T]he Due Process Clause of the Fifth Amendment also does not permit convicting an accused of an offense with which he has not been charged.” United States v. Girouard, 70 M.J. 5, 10 (C.A.A.F.2011).
We granted review to determine whether the offense of indecent acts was a lesser included offense of aggravated sexual assault. We conclude that, as charged in this case, indecent acts (committing a sexual act in an open and notorious manner) is not a lesser included offense of aggravated sexual assault (engaging in a sexual act with an incapacitated person). It was therefore error for the military judge to instruct on indecent acts.
We also granted an issue as to whether the adultery specification charged under Article 134 failed to state an offense because it did [193]*193not expressly allege the terminal element.1 We conclude that the record of trial demonstrates that Tunstall was on actual notice of the terminal element and therefore that he was not prejudiced by its omission. See United States v. Humphries, 71 M.J. 209 (C.A.A.F.2012).
Background
In April of 2009, Tunstall and Airman KAS, who were assigned to Hurlburt Field, Florida, were with a group of airmen who spent the day drinking at the beach and in an Air Force dormitory. The two were flirting throughout the afternoon and later were involved in a drinking game with two other airmen in the dorm. The airmen became drunk and during the drinking game KAS removed her clothes and straddled Tunstall, who began to digitally penetrate her vagina in the presence of the two other airmen. The Government considered this episode of sexual activity to be consensual. Shortly thereafter, however, KAS fell to the floor and began to vomit. At this point KAS was described as conscious but not vocal or making any actions. Tunstall and another airman helped KAS to a sink where she continued to have the dry heaves. While KAS was leaning over the sink Tunstall digitally penetrated her vagina until the other airman said, “[i]t’s not time for that. I mean she’s sick. We need to take care of her.” Tun-stall and another airman then helped KAS to the bathroom. During this period KAS was described as definitely intoxicated and rolling in and out of consciousness. Tunstall then locked himself in the bathroom with KAS and had sexual intercourse with her in the shower.2
Specification 2 of Charge I charged Tun-stall with aggravated sexual assault under Article 120 for the digital penetration of KAS’s vagina while she was leaning over the sink and while she was substantially incapable of declining participation. During his instructions on findings, the military judge sua sponte instructed the members that the offense of indecent acts was a lesser included offense of the charged offense of aggravated sexual assault. Tunstall was acquitted of aggravated sexual assault under Specification 2 of Charge I, but was found guilty of the lesser included offense of indecent acts.
Tunstall did not object to the instruction at trial, but on appeal to the CCA he argued that the military judge erred in giving a lesser included offense instruction for the offense of indecent acts. Tunstall, No. ACM 37592, slip op. at 7-11. The CCA held that the offense of indecent acts was a lesser included offense of aggravated sexual assault. Id. at 11. Although the lower court did not conduct an element-by-element comparison of the charges, it concluded that “one cannot engage in a ‘sexual act’ with someone who was vomiting in a sink in the presence of a third party without also engaging in an indecent act.” Id. at 10.
Issue I
Lesser Included Offense
Whether an offense is a lesser included offense is a question of law that is reviewed de novo. United States v. Girouard, 70 M.J. 5, 9 (C.A.A.F.2011). While the granted issue frames our analysis in terms of a lesser included offense, we believe that this ease raises important instructional and notice issues as well.
Because there was no objection to the instruction at trial, we review for plain error. United States v. Wilkins, 71 M.J. 410, 412 (C.A.A.F.2012) (citing United States v. Arriaga, 70 M.J. 51, 54 (C.A.A.F.2011)). Under a plain error analysis, the accused “has [194]*194the burden of demonstrating that: (1) there was error; (2) the error was plain or obvious; and (3) the error materially prejudiced a substantial right of the accused.” Girouard, 70 M.J. at 11.
This court applies the elements test to determine whether one offense is a lesser included offense of another. United States v. Jones, 68 M.J. 465, 468 (C.A.A.F.2010).
Under the elements test, one compares the elements of each offense. If all of the elements of offense X are also elements of offense Y, then X is an LIO of Y. Offense Y is called the greater Offense because it contains all of the elements of offense X along with one or more additional elements.
Id. at 470.
The elements of aggravated sexual assault under Article 120, as charged in this case, are: (1) that the accused engaged in a sexual act with another person; and (2) the other person was substantially incapable of declining participation in the sexual act. Manual for Courts-Martial, United States pt. IV, para. 45.b.(3)(c) (2008 ed.) (MCM). Specification 2 of Charge I alleged that Tun-stall:
did ... engage in a sexual act, to wit: digital penetration by [Tunstall] of the vagina, with [A1C KAS], who was substantially incapable of declining participation in the sexual act.
During his instructions on findings the military judge instructed the members on the offense of indecent acts as a lesser included offense of aggravated sexual assault:
Indecent act under Article 120. You are advised a lesser included offense of the offense alleged in Specification 2 of Charge I is the offense of indecent acts, also a violation of Article 120. In order to find the accused guilty of this lesser included offense, you must be convinced by legal and competent evidence beyond reasonable doubt:
One, that on or about 17 April 2009, at or near Hurlburt Field, Florida, the accused engaged in certain wrongful conduct, to wit: digital penetration of the vagina of Airman [KAS]; and
Two, that the conduct was indecent.
After providing the members with definitions of relevant terms, the military judge went on to instruct the members:
Article 120, UCMJ, is not intended to regulate the wholly private consensual activities of individuals. In the absence of aggravating circumstances, private consensual sexual activity[,] including sexual intercourse^] is not punishable as an indecent act. Among possible aggravating circumstances is that the sexual activity was open and notorious. Sexual activity may be open and notorious when the participants know that someone else is present. This presence of someone else may include a person who is present and witnesses the sexual activity, or is present and aware of the sexual activity through senses other than vision. On the other hand, sexual activity that is not performed in the close proximity of someone else, and which passes unnoticed, may not be considered open and notorious. Sexual activity may also be considered open and notorious when the act occurs under circumstances in which there is a substantial risk that the acts could be witnessed by someone else, despite the fact that no such discovery occurred.
This lesser included offense differs primarily from the charged offense in Specification 2 of Charge I in that this offense does not require as an essential element that the accused digitally penetrated Airman First Class [KAS] when she was substantially incapable of declining participation in the sexual act. This lesser included offense, however, does require you to determine whether the act itself was indecent.
The elements of the lesser included offense of “indecent acts” are: (1) the accused engaged in certain conduct; and (2) the conduct was indecent. MCM pt. IV, para. 45.b.(ll) (2008 ed.).
The Government notes that the offense of indecent acts occurs when any person engages in “indecent conduct,” which is defined as “that form of immorality relating to sexual impurity that is grossly vulgar, obscene, and [195]*195repugnant to common propriety, and tends to excite sexual desire or deprave morals with respect to sexual relations.” Article 120(t)(12), UCMJ. The Government goes on to argue that the aggravated sexual assault specification at issue could, without alteration, constitute a legally sufficient indecent acts specification. The crux of the Government’s argument is that the act alleged in Specification 2 of Charge I constituted indecent conduct under the above definition because KAS was “substantially incapable of declining the participation in the sexual act.”
Rather than reflecting a greater/lesser relationship, however, the Government’s theory results in alternative offenses which criminalize the same conduct. It has long been recognized that a jury must be able to rationally acquit on the greater offense but still convict on the lesser offense. Sansone v. United States, 380 U.S. 343, 350, 85 S.Ct. 1004, 13 L.Ed.2d 882 (1965) (“[T]he lesser offense must be included within but not, on the facts of the case, be completely encompassed by the greater. A lesser-included offense instruction is only proper where the charged greater offense requires the jury to find a disputed factual element which is not required for conviction of the lesser-included offense.”).3
As charged in this case and under the Government’s lesser included theory, there is no additional fact that the members would need to find in order to convict for the offense of aggravated sexual assault which would be unnecessary to convict for the offense of indecent acts. Neither requires a factual finding which the other does not. The first element of both offenses is established by the same set of facts: the “sexual act” (aggravated sexual assault) and “certain conduct” (indecent acts) refer to the digital penetration of KAS’s vagina. The second element of each offense is also established by the same alleged fact: KAS was substantially incapable of declining participation (aggravated sexual assault); and the conduct was indecent because KAS was substantially incapable of declining participation (indecent acts). The MCM in effect at the time recognized that treating indecent acts as a lesser included offense of aggravated sexual assault is appropriate “[djepending on the factual circumstances in each case,” MCM pt. IV, para. 45.e. (2008 ed.). Under the facts of this case, where there is no additional fact that the members would need to find in order to establish the offense of aggravated sexual assault which would be unnecessary to establish the offense of indecent acts, the two offenses do not stand in a relationship of greater/lesser offense, because a rational trier of fact could not acquit on the greater offense and convict on the lesser offense.4 It was therefore plain and obvious error for the military judge to sua sponte give the lesser included offense instruction.
The military judge compounded the error with his further instructions on indecent acts. The military judge instructed the members that engaging in a sexual act in the presence of others is considered “open and notorious” behavior which could constitute an indecent act. “Open and notorious” is not a basis or theory for the offense of aggravated [196]*196sexual assault, and that instruction was the first mention in the trial of the “open and notorious” theory. The military judge went on to instruct the members that the greater offense of indecent acts differed from the offense of aggravated sexual assault as it did not require them to find that KAS was substantially incapable of declining participation, but only that the act itself was indecent.
In providing these instructions, the military judge essentially took the “substantially incapable of declining participation” theory for the offense of indecent acts off the table and instead provided the members with detailed instructions as to the “open and notorious” theory for the offense. This error resulted in material prejudice to Tunstall. We agree with the CCA that under the circumstances of this case, the members convicted Tunstall of indecent acts under an “open and notorious” theory. Tunstall, No. ACM 37592, slip op. at 10 (“Under the facts of this case, we conclude that one cannot engage in a ‘sexual act’ with someone who was vomiting in a sink in the ‘presence of a third party without also engaging in an indecent act.” (emphasis added)). However, the due process principle of fair notice mandates that “an accused has a right to know what offense and under what legal theory” he will be convicted. Jones, 68 M.J. at 468 (quoting Medina, 66 M.J. at 26-27) (emphasis added). As Tunstall was neither charged with nor on notice of the offense of indecent acts under the “open and notorious” theory until the military judge’s instruction, he was not on fair notice to defend against that offense and his due process rights were violated.5
Because the military judge instructed on an offense which was not a “lesser included” offense and because the military judge instructed on a theory of indecency of which Tunstall was not on notice, the findings with regard to Specification 2 of Charge I are set aside and the case is remanded to the CCA to reassess the sentence or return the case to the convening authority for a rehearing on sentence.6
Issue II
The Foster,/Humphries Issue
Tunstall argues that the Article 134 adultery specification in Charge II failed to state an offense because it did not expressly allege the terminal element. In the context of an adultery specification, the government may prove the terminal element in one of two ways — either that, under the circumstances, the adulterous conduct was to the prejudice of good order and discipline or that it was of a nature to bring discredit upon the armed forces. MCM pt. IV, para. 62.c.(2). As Tun-stall failed to object to the adultery specification at trial, we review for plain error. To establish plain error, an appellant has the burden to demonstrate: (1) there was error; (2) the error was plain or obvious; and (3) the error materially prejudiced a substantial right of the accused.7 Humphries, 71 M.J. [197]*197at 214. We have held that failure to allege the terminal element constitutes plain and obvious error and resolution of the case will depend upon whether “the error has prejudiced the substantial rights of the accused.” United States v. Ballan, 71 M.J. 28, 30 (C.A.A.F.2012).
In Humphries, we stated that “we look to the record to determine whether notice of the missing element is somewhere extant in the trial record, or whether the element is ‘essentially uncontroverted.’ ” 71 M.J. at 215-16. In making this inquiry, courts are limited to considering evidence contained in the trial record. Id.
While the terminal element of Article 134 was not discussed during voir dire, the opening statements, or the Government’s case-in-chief, it was raised by the defense during trial. At the start of the defense ease, the senior defense counsel sought the admission of a petition for simplified dissolution of marriage. The dissolution of marriage is relevant to marital status, which is one factor to be considered as to whether the terminal element is met. MCM pt. IV, para. 62.e.(2)(a). When the senior trial counsel objected to its admission, the senior defense counsel explained that the document was relevant to the third element of the offense of adultery — that “under the circumstances that conduct, the adultery, was prejudicial to good order and discipline, or service discrediting.” The military judge admitted the document.
Before closing arguments, the military judge provided the parties with copies of his instructions. The instructions listed the third element of the adultery offense as “that under the circumstances, the conduct of the accused was to the prejudice of good order and discipline in the armed forces or was of a nature to bring discredit upon the armed forces.” He then defined the terms “conduct prejudicial to good order and discipline” and “service discrediting conduct,” and explained how the evidence needed to establish one but not both of those terms. The military judge asked if there were any objections. Other than to the definition of “substantially incapable,” the defense counsel stated, “No, sir.”
In closing argument on the adultery specification, the defense counsel focused on the third element. He asked the members to read the military judge’s instructions explaining conduct prejudicial to good order and discipline and conduct of a nature to bring discredit upon the armed forces. He asserted that, because the Government had not called any witnesses to prove the third element, it failed to prove that Tunstall was guilty of adultery. Here, where evidence in the trial record indicates that the defense introduced evidence for the specific purpose of negating both theories of the terminal element of Article 134, UCMJ, and further argued that the Government had not proven either terminal element during its closing argument, we conclude that Appellant has not met his burden to demonstrate material prejudice to a substantial right, as he did defend himself, despite the Government’s error.8
[198]*198
Decision
The decision of the United States Air Force Court of Criminal Appeals is reversed as to Charge I, Specification 2, the finding as to that specification is set aside, and that specification is dismissed. The remaining findings are affirmed. The decision as to the sentence is set aside and the record is returned to the Judge Advocate General of the Air Force for remand to that court for further proceedings consistent with this opinion.