Question: Glen of Imaal Terrier and Appenzeller Sennenhund, are a breed of what?

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Glen of Imaal Terrier: The Glen of Imaal Terrier () is a breed of dog of the terrier category and one of four Irish terrier breeds.  It is sometimes called the Irish Glen of Imaal Terrier or the Wicklow Terrier, and the name of the breed is often shortened by fanciers to just Glen.

Rare breed (dog): Rare breed (dog) is any breed of dog that is small in number and is used to refer to both old established breeds such as the Stabyhoun and Glen of Imaal Terrier or newer creations.  Since dogs have greater genetic variability than other domesticated animals the number of possible breeds is vast with new crosses constantly occurring, from these both selected and random crosses may come new breeds should offspring reliably breed true to type.  New breeds from the wild such as the Carolina Dog are quite rare compared to attempts at breed creation from man as found in the American Hairless Terrier which sought to exploit a mutation.

Russkiy Toy: The Russian Toy (also known as the Russian Toy Terrier, and in Russia as the Russkiy Toy, Toychik,Russian: Русский той, Тойчик ) is a very small breed of dog originally bred in Russia from the English Toy Terrier which is known today as the Manchester Terrier.  There are two types of coats in the breed: smooth coat and long coat.  The smooth-coated variety was previously known as the Russian Toy Terrier and long-coated as the Moscow Long Haired Toy Terrier.  Both were brought together under the same Russian Toy Terrier name in 1988 and the "Terrier" was dropped from the name when the breed was added in 2006 to the official list of breeds registered with the Fédération Cynologique Internationale and has been registered in the Foundation Stock Service of the American Kennel Club since 2008, allowed to compete in AKC companion events since 2010.  The first official breed standard of the two varieties was written in 1966 in Russia.

Appenzeller Sennenhund: The Appenzeller Sennenhund is a medium-size breed of dog, one of the four regional breeds of Sennenhund-type dogs from the Swiss Alps.  The name Sennenhund refers to people called "Senn", herders in the Appenzell region of Switzerland.

American Russell Terrier Club: The American Russell Terrier Club (formerly named the English Jack Russell Terrier Club), founded by JoAnn Stoll in 1995, was the first registry in the United States to maintain the Russell Terrier as a separate breed from the Parson Russell Terrier.  The American Jack Russell Terrier Club is affiliated with both the United Kennel Club and the American Kennel Club.  The purpose of the early founders was to establish a registry for the perpetuation and development of the Russell Terrier as a pure strain of working Jack Russell Terrier keeping their blood and type pure within the registry to works towards Kennel Club recognition as an official breed in the US.  On January 1, 2001, the United Kennel Club recognized the Russell Terrier as an official breed, designating only the stock from the American Russell Terrier Club as Foundation stock for the UKC Russell Terrier.  In 2004 the American Russell Terrier Club submitted an official request to include the American Russell Terrier Club stock into the AKC FSS Program to work towards becoming an official breed under the perimeters.  On December 8, 2004, the AKC officially accepted the Russell Terrier.

Appenzeller (chicken): The Appenzeller is a breed of chicken originating in Appenzell region of Switzerland.  The Appenzeller comes in two varieties.  The Spitzhauben variety, meaning "pointed hood", has a V-comb and feather crests in males and females.  The word 'spitzhauben' derives from the frilly hat worn by the women in the Appenzeller region in Switzerland.  The breed was imported into America by a doctor.  The Barthuhner ("bearded hen") has a rose comb and no crest.  Both types appear in either black, golden spangled and silver spangled plumage.  They are mostly a show breed, but are decent egg layers.  They lay small white eggs about 5 times per week.

Terrier Group: Terrier Group is the name of a breed Group of dogs, used by kennel clubs to classify a defined collection of dog breeds.  In general, a "Terrier Group" includes one particular type of dog, the Terrier, although other types may be included in a kennel club's "Terrier Group".  Most major English-language kennel clubs include a "Terrier Group" although different kennel clubs may not include the same breeds in their "Terrier Group".  The international kennel club association, the Fédération Cynologique Internationale, includes Terriers in Group 3 "Terrier", which is then further broken down into four "Sections" based on the type of terrier and breed history.

Airedale Terrier: The Airedale Terrier (often shortened to "Airedale"), also called Bingley Terrier and Waterside Terrier, is a dog breed of the terrier type that originated in the valley ("dale") of the River Aire, in the West Riding of Yorkshire, England.  It is traditionally called the "King of Terriers" because it is the largest of the terrier breeds.  The Airedale was bred from the Old English Black and Tan Terrier (now extinct), the Bull Terrier, the Otterhound and probably some other Terrier breeds, originally to serve as an all around working farm dog.  In Britain this breed has also been used as a war dog, guide dog and police dog.  In the United States, this breed has been used to hunt big game, upland birds, and water fowl, and serve in many other working capacities.

Teddy Roosevelt Terrier: The Teddy Roosevelt Terrier is a small to medium-sized American hunting terrier.  Lower-set with shorter legs, more muscular, and heavier bone density than its cousin the American Rat Terrier.  There is much diversity in the history of the Teddy Roosevelt Terrier breed and it shares a common early history with the American Rat Terrier, Fox Paulistinha and Tenterfield Terrier.  It is said the Rat Terrier background stems from the terriers or other dogs that were brought over by early English and other working class immigrants.  Since the breed was a farm, hunting and utility dog there was little to no planned breeding other than breeding dogs with agreeable traits to each other in order to produce the desired work ethic in the dog.  It is assumed that the Feist (dog), Bull Terrier, Smooth Fox Terrier, Manchester Terrier, Whippet, Italian Greyhound, the now extinct English White Terrier, Turnspit dog and or Wry Legged Terrier all share in the Teddy Roosevelt Terrier's ancestry.  These early Ratting Terriers were then most likely bred to the Beagle or Beagle cross bred dogs (for increased scenting ability) and other dogs.  Maximizing the influences from these various breeds provides the modern Teddy Roosevelt Terrier with a keen sense of awareness and prey drive, an acute sense of smell and a very high intellect.  Although they tend to be aloof with strangers they are devoted companion dogs with a strong desire to please and be near their owners side at all times.

Turnspit dog: The Turnspit dog was a short-legged, long-bodied dog bred to run on a wheel, called a turnspit or dog wheel, to turn meat.  The type is now extinct.  It is mentioned in "Of English Dogs" in 1576 under the name "Turnespete".  William Bingley's "Memoirs of British Quadrupeds" (1809) also talks of a dog employed to help chefs and cooks.  It is also known as the Kitchen Dog, the Cooking Dog, the Underdog and the "Vernepator".  In Linnaeus's 18th century classification of dogs it is listed as "Canis vertigus".  The breed was lost since it was considered to be such a lowly and common dog that no record was effectively kept of it.  Some sources consider the Turnspit a kind of Glen of Imaal Terrier, others make it a relative of the Welsh Corgi.

Supporting paragraphs: Glen of Imaal Terrier Appenzeller Sennenhund
Answer: dog