For syrup, combine water and sugar in pan. Stir over medium heat until sugar dissolves. Increase heat and bring to boil. Boil without stirring for 5 minutes. Cool syrup, then cover and refrigerate until needed.
Peel, seed, and chop melon. Puree in food processor(about 4 cups.) In a bowl mix puree, sugar syrup, and lime juice. Freeze in ice cream maker according to instructions. Then freeze in freezer 2-3 hours to firm it up. Garnish with lime slice and mint.
