THE ALOPEKOS TEUMESIOS was a gigantic Fox which sent by the gods to the countryside of Thebes as punishment for some crime. Kreon, the then Regent of Thebes, set Amphitryon the impossible task of destroying the beast - impossible because the fox was destined never to be caught. The hero discovered a solution to the problem by setting the magical dog Lailaps to the hunt, an animal which was destined always to catch its quarry.

Zeus faced with a contradiction in fate (an uncatchable fox being pursued by an unavoidable dog) turned the pair of beasts to stone or perhaps placed them amongst the stars as the Constellations Canis Major (Lailaps) and Canis Minor or Lepus (the Fox). Their contest was in this way either frozen or set to play out for eternity.

Homerica, The Epigoni Frag 2 (from Photius, Lexicon s.v. Teumesia) (trans. Evelyn-White) (Greek epic C7th B.C.) :
"Teumesia. Those who have written on Theban affairs have given a full account of the Teumesian Fox (Alopekos Teumesia). They relate that the creature was sent by the gods to punish the descendants of Kadmos, and that the Thebans therefore excluded those of the house of Kadmos from the kingship. But they say a certain Kephalos, the son of Deion, an Athenian, who owned a Hound [Laelaps] which no beast ever escaped, had accidentally killed his wife Prokris, and being purified of the homicide by the Kadmeans, hunted the Fox with his Hound, and when they had overtaken it both Hound and Fox were turned into stones near Teumessos. These writers have taken the story from the Epic Cycle."

Pseudo-Apollodorus, Bibliotheca 2. 57 (trans. Aldrich) (Greek mythographer C2nd A.D.) :
"[Amphitryon, the step-father of Herakeles] undertook a campaign against the Teleboans, inviting Kreon [king of Thebes] to join him. Kreon agreed to do so, if first Amphitryon would free the Kadmeian Land [Thebes] of its Fox. For a wild Fox was creating havoc in the land. But despite Amphitryon’s attempts, it was fated that no one would subdue this Fox. As the land continued in torment, the Thebans once a month would set out one of the citizen’s children for it, for otherwise it would have seized many of them. Amphitryon went to Deioneus’ son Kephalos at Athens, and after promising him a share of the booty from the Teleboan expedition, persuaded him to bring to the fox- hunt the Dog [Laelaps] which Prokris had received from Minos and brought from Krete, for it was also fated that this Dog would catch whatever it chased. Consequently, when the Fox was chased by the Dog, Zeus turned them both to stone [the only solution to the contradictory fates of a Fox destined never be caught being chased by a dog destined to catch whatever it chased]."

Pausanias, Description of Greece 9. 19. 1 (trans. Jones) (Greek travelogue C2nd A.D.) :
"On this highway is a place called Teumessos, where it is said that Europa was hidden by Zeus. There is also another legend, which tells of a Fox called the Teumessian Fox, how owing to the wrath of Dionysus the beast was reared to destroy the Thebans, and how, when about to be caught by the Hound [Lailaps] given by Artemis to Prokris the daughter of Erekhtheus, the Fox was turned into a stone, as was likewise this Hound."

Antoninus Liberalis, Metamorphoses 41 (trans. Celoria) (Greek mythographer C2nd A.D.) :
"Amphitryon who needed the dog [Lailaps who always caught his quarry], went to Kephalos and asked him if he would be willing to join him, with the dog, in going after the [Teumessian] Fox. He promised to hand over to him a share of the booty which he would take from the Teleboans.
For at that time there had appeared in the land of the people of Kadmos, a Fox was a monstrous creature. It would regularly issue out of Teumessos snatching up Kadmeans. Every thirty days they would put out a child for it and the Fox would take it and eat it up.
Amphitryon had asked Kreon and the Kadmeans to help in making war against the Teleboians. They refused unless he helped them do away with the Fox. Amphitryon accepted these conditions from the Kadmeans and went to Kephalos and told him about the agreement and urged him to go to Thebes with the dog. Kephalos accepted the proposal and set out to hunt the Fox.
But it had been ordained that the Fox could not be taken by any hunter, and that nothing should escape that dog when it went hunting. Zeus saw them when they reached the plain of Thebes and turned them both into stones."

Pseudo-Hyginus, Astronomica 2. 35 (trans. Grant) (Roman mythographer C2nd A.D.) :
"The Dog [Laelaps] was so swift that no beast could escape . . . Cephalus brought it to Thebes with him when he came. There was a Fox there which was said to be so swift that it could outrun all dogs. So when the two animals met, Jupiter [Zeus], in a dilemma, as Istrus says, changed them both to stone."

Ovid, Metamorphoses 7. 748 ff (trans. Melville) (Roman epic C1st B.C. to C1st A.D.) :
"The riddle that had baffled earlier brains was solved by Laiades [Oidipous son of Laius] and headlong down the Carmina [Sphinx] had fallen, her mysteries forgotten. At once a second plague was launched on Thebae Aoniae, a savage beast [the Teumessian Fox] that killed and feasted on the farmfolk and their flocks. We, the young squires, ringed the broad pastures with our hunting nets, but with a bound the beast was over them, clearing the tops of our entanglements. We slipped our dogs; the beast, as they gave chase, fled like a bird and mocked our hundred hounds. With one accord my comrades called to me for Laelaps (Whirlwind) (my find gift-hound), who for long had fought the leash that checked him. He was loosed and straightway lost to sight; the hot dust held his footprints; he had vanished; not so swift a lance’s flight or bullets from a sling or slender arrows from a Cretan bow. Some rising ground commanded the wide fields; I climbed the top and gained a grandstand view of that strange chase; one moment the beast’s caught the next the death-wound’s missed him--he’s escaped. His course was cunning, never straight for long; he doubled back and circled to deceive the chasing jaws, to foil his foe’s assault. The hound pressed close, clung step for step; it seemed he’d got him, but he failed and snapped the air. My javelin must help, I thought, and while I weighed it in my hand and tried to fit my fingers in the loop, I glanced aside, and when I looked again--amazing sight!--there in the open plain below I saw two marble statues, one of them, you’d swear, in flight, the other pouncing on its prey. Some god, if gods were watching, must have willed that both should be unbeaten in that chase."