Question: Are The Knot Garden and Ariadne auf Naxos both operas?
Context: Trudeliese Schmidt (7 November 1942 − 24 June 2004) was a German operatic mezzo-soprano who had an international career, performing at major opera houses and festivals in Europe.  The singer with a remarkable stage presence excelled in trouser roles such as Cherubino, Idamante, Hänsel, Octavian and the composer in "Ariadne auf Naxos".  She performed in premieres of operas by Isang Yun and Manfred Trojahn. Ariadne auf Naxos ("Ariadne on Naxos"), Op.  60, is an opera by Richard Strauss with a German libretto by Hugo von Hofmannsthal.  Combining slapstick comedy and consummately beautiful music, the opera's theme is the competition between high and low art for the public's attention. The Visitors is an opera in three acts and a prologue composed by Carlos Chávez to an English libretto by the American poet Chester Kallman.  The work was Chávez's only opera.  Its first version, with the title "Panfilo and Lauretta", premiered in New York City in 1957.  The final version with the title "The Visitors" was premiered in Guanajuato, Mexico in 1999, twenty years after the composer's death.  The story is set in 14th century Tuscany during the time of the Black Death.  The libretto (like those for "Pagliacci" and "Ariadne auf Naxos") uses the device of a play within a play to reflect and intensify the relationships between the protagonists, who in this case are loosely based on characters in "The Decameron". Ariadne auf Naxos ("Ariadne on Naxos") is a duodrama in one act by Czech composer Jiří Antonín Benda (also Georg Benda) with a German libretto by .  It was commissioned by Abel Seyler, whose theatrical company arrived in Gotha in 1774.  The opera's first performance was at the Schloss Friedenstein, Gotha, on 27 January 1775. Erna Ellmenreich (30 May 1885 – 14 April 1976) was a German operatic soprano, a member of the Staatstheater Stuttgart.  She performed there leading parts and several premieres, including "Ariadne auf Naxos" by Strauss and works by Paul Hindemith. Ellen Shade is an American operatic soprano from New York.  Her repertoire includes the Kaiserin in "Die Frau ohne Schatten", the Marschallin "Der Rosenkavalier", Chrysothemis "Elektra", Ariadne "Ariadne auf Naxos", Arabella, Katya Kabanova, Aida, Desdemona "Otello", Amelia "Un ballo in Maschera", Amelia "Simon Boccanegra", Sieglinde "Die Walkure", Elsa "Lohengrin", Elisabeth "Tannhauser", Eva "Die Meistersinger von Nurnberg".  In Europe she has appeared at La Scala Milan, the Royal Opera House, Covent Garden, the Bastille and the Chatelet in Paris and in Vienna, Salzburg Festival, Berlin, Hamburg, Frankfurt [Article Reference], Stuttgart, Amsterdam, Brussels, Geneva and Athens.  In North America she has performed with virtually all the major opera companies, including the Metropolitan Opera New York, Chicago, San Francisco, Los Angeles, Houston, Dallas, Seattle, Santa Fe, and the Canadian Opera in Toronto. Glenn Winslade (born 1958) is an Australian operatic tenor known for his interpretations of dramatic roles such as Florestan in "Fidelio", the title role in "Idomeneo", the title role in "La clemenza di Tito", Erik in "The Flying Dutchman", the title role in "Rienzi", the title role in "Lohengrin", the title role in "Tannhäuser", the Emperor in "Die Frau ohne Schatten", Apollo in "Daphne", Bacchus in "Ariadne auf Naxos" and Max in "Der Freischütz". Margarethe Siems (20 December 1879 – 13 April 1952) was a German operatic soprano and voice teacher.  A Kammersängerin of the Dresden State Opera, between 1909 and 1912 Siems created leading roles in three operas by Richard Strauss: Chrysothemis in "Elektra", the Marschallin in "Der Rosenkavalier", and Zerbinetta in "Ariadne auf Naxos". The Knot Garden is the third opera by composer Michael Tippett for which he wrote the original English libretto.  The work had its first performance at the Royal Opera House, Covent Garden, on 2 December 1970 conducted by Sir Colin Davis and produced by Sir Peter Hall.  There is a recording with the original cast. Norine Burgess is a Canadian singer.  She is a graduate of the University of Calgary and the University of Toronto’s Opera School, mezzo-soprano.  She received additional training as a member of the Canadian Opera Company (COC) Ensemble where she appeared in Electra, Suor Angelica, Lulu and Der Rosenkavalier.  Ms. Burgess also performed Le Nozze di Figaro(Cherubino), Ariadne auf Naxos (Dryad), La Traviata(Flora) and Die Zauberflöte (Second Lady) with the COC.  Additional operatic successes include Le Nozze di Figaro (Cherubino) and Carmen (Mercedes) with the Vancouver Opera, Fenena in Nabucco with Manitoba Opera, Albert Herring (Nancy) with the Calgary Opera and many appearances with the Edmonton Opera.
Answer: yes