Question: Are the Lancashire Heeler and the Glen of Imaal Terrier both listed by the Kennel Club (UK) as a vulnerable breed?
Context: 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. The Yorkshire Terrier is a small dog breed of terrier type, developed during the 19th century in Yorkshire, England, to catch rats in clothing mills.  The defining feature of the breed is its maximum size of 7 lb , although some may exceed this and grow up to 15 lb .  It is placed in the Toy Terrier section of the Terrier Group by the Fédération Cynologique Internationale and in the Toy Group or Companion Group by other kennel clubs, including the American Kennel Club.  A popular companion dog, the Yorkshire Terrier has also been part of the development of other breeds, such as the Australian Silky Terrier.  It has a grey, black, and tan coat, and the breed's nickname is "Yorkie". 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. 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. 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. The American Hairless Terrier is a rare breed of dog that was derived as a variant of Rat Terrier.  As of January 1, 2004, the United Kennel Club deemed the AHT a separate terrier breed, granting it full UKC recognition.  An intelligent, social and energetic working breed, the American Hairless Terrier is often listed as a potential good breed choice for allergy sufferers. The Lancashire Heeler is a small breed of dog developed for use as a drover and herder of cattle.  The Lancashire Heeler is listed by the Kennel Club (UK) as a vulnerable breed. 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. 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. The Toy Manchester Terrier is a breed of dog, categorized as a terrier.  The breed was bred down in size in North America from the Manchester Terrier, and is placed in the Toy Group by the American Kennel Club and the Canadian Kennel Club (the Manchester Terrier is placed in the Terrier Group.)  Neither the Fédération Cynologique Internationale nor The Kennel Club recognize a Toy variety of the Manchester Terrier.
Answer: no