Two pints from 7 and 11 pint jugs

You need exactly $2$ pints of water from a stream, but only have an unmarked $7$-pint jug and an unmarked $11$-pint jug. A move is filling a jug, emptying a jug, or pouring from one jug into the other. What is the smallest number of moves that leaves exactly $2$ pints in one jug?

14. Repeatedly fill the $7$-pint jug and tip it into the $11$, emptying the $11$ whenever full; the amounts left behind go $3,6,2$ (adding $7$ modulo $11$). A breadth-first search over jug states confirms that $14$ moves is the minimum.