First fully automated test run of barter-set algorithm:
Suppose the category is girls names, and each person knows only 5 names:
User knows: betty, susan, mary, joyce, patricia.
Host knows: susanna, susan, marie, joan, wilma.
(This is the same initial knowledge-state as the manually-worked-out example.)
(Note that ^ at end of line means that player doesn't know the rest of any
 word that starts with the part in brackets, so instead of adding a letter to
 that word the player will switch to another sequence on the next line below.)
(Note that whenever either player finishes a word, by entering . instead of
 a letter, that player next must immediately start another word. Whenever
 either player starts or extends a prefix that is already shared, that player
 next must immediately extend it, repeatedly until a new letter gets added or
 the word is finished.)
Here's program output, except last character in each "User" line is user input.
User: []b
Host: [b]^
Host: []m
User: [m]a
Host: [ma]r
User: [mar]y
Host: [mary]^
Host: []s
User: [s]u
Host: [su]s
User: [sus]a
Host: [susa]n
User: [susan].
User: [mary].
User: [b]e
Host: [be]^
Host: [susan]n
User: [susann]^
User: [be]t
Host: [bet]^
Host: [susann]a
User: [susanna]^
User: [bet]t
Host: [bett]^
Host: [susanna].
Host: []j
User: [j]o
Host: [jo]a
User: [joa]^
User: [bett]y
Host: [betty]^
Host: [joa]n
User: [joan]^
User: [betty].
User: []j
User: [j]o
User: [jo]y
Host: [joy]^
Host: [joan].
Host: []m
Host: [m]a
Host: [ma]r
Host: [mar]i
User: [mari]^
User: [joy]c
Host: [joyc]^
Host: [mari]e
User: [marie]^
User: [joyc]e
Host: [joyce]^
Host: [marie].
Host: []w
User: [w]^
User: [joyce].
User: []p
Host: [p]^
Host: [w]i
User: [wi]^
User: [p]a
Host: [pa]^
Host: [wi]l
User: [wil]^
User: [pa]t
Host: [pat]^
Host: [wil]m
User: [wilm]^
User: [pat]r
Host: [patr]^
Host: [wilm]a
User: [wilma]^
User: [patr]i
Host: [patri]^
Host: [wilma].
Host: []marie. (and 4 more) *already*shared*
:host-quits