1. A recognition system comprising: processing circuitry coupled to a memory, the processing circuitry being configured to: receive a first model that converts subwords serving as elements of words into the words, the subwords being one or more phonemes or one or more syllables; produce, on the basis of the first model, a first finite state transducer that includes a first path having transitions converting one or more first subwords into one or more first words and a second path having cyclic paths to which one or more second subwords are assigned and a transition to which a class is assigned, a first state of the second path being the same as a first state of the first path; produce a third finite state transducer by composing the first finite state transducer with a second finite state transducer produced on the basis of a language model that includes the class; and produce a fifth finite state transducer by composing the third finite state transducer with a fourth finite state transducer, the fourth finite state transducer being produced on the basis of a second model and including a third path, the second model including an additional word, one or more subwords and the class that corresponds to the additional word; and a searcher configured to recognize a second word corresponding to an input speech by using the fifth finite state transducer, wherein the searcher outputs the second word other than the additional word, without performing conversion by the fourth finite state transducer, and outputs the additional word that is an output symbol on a fourth path of the fifth finite state transducer, the fourth path is generated by composing a fifth path of the third finite state transducer with the third path, one of the output symbols on the third path is the additional word, an input symbol string on the third path includes one or more third subwords and the class, and corresponds to an output symbol string of the fifth path, and the class which appears in the input symbol string on the third path and appears in the output symbol string of the fifth path controls an appearance location of the additional word.