1. A speech recognition system, comprising: a speech input device configured to input a speech as an input speech by converting the speech to an electric signal; and a speech recognition device configured to take in and recognize the speech input to the speech input device, wherein the speech input device and the speech recognition device are communicatively connected to each other, wherein the speech input device comprises: a user dictionary section storing words for use with recognition of the input speech; and a reduced user dictionary creation unit configured to create a reduced user dictionary by extracting words corresponding to the input speech from the user dictionary section, and wherein the speech recognition device comprises: a speech recognition unit configured to input the input speech and the reduced user dictionary from the speech input device and recognize the input speech based on the reduced user dictionary and a built-in system dictionary storing words for speech recognition, wherein the reduced user dictionary creation unit includes: a comparing section which compares the input speech and a word in the user dictionary and compiles a likelihood of each word appearing in the input speech, a word temporarily storing section which temporarily stores a set of each word and a corresponding likelihood compiled, and a word selection section which selects one or a plurality of words having high usage from the word temporarily storing section to thereby create the reduced user dictionary.