11. The character conversion process according to claim 10 , wherein a first image and a second image are concurrently displayed by the display device, a part of the plurality of conversion candidates being displayed in the first image in order of frequency of use on the basis of the frequency-of-use information, and a rest of the plurality of conversion candidates being displayed in the second image in the determined order of display of the plurality of conversion candidates.
10. The character conversion process according to claim 7 , wherein the conversion database stores frequency-of-use information indicating frequency of previous use of converted data items, the frequency-of-use information is updated according to confirmation of one of the plurality of conversion candidates as the converted data item, and in a case where conversion candidates searched out includes a character which immediately follows the one or more already inputted characters and total number of times the character input key is to be pressed down before inputting the character is identical to each other in the searched out conversion candidates, an order of display of the searched out conversion candidates is determined so that the total number of times one of the one or more select keys is to be pressed down before selecting each of the searched out conversion candidates decreases with increase in frequency of previous use of the searched out conversion candidates.