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I deeply appreciate Professor Nobuyoshi Asai who gave me his opinions and advice in this research. I also appreciate all members of the Mathematical Foundation of Computer Science Laboratory, Kou Ishikawa, Toshiyuki Oowada, Shingo Ootake, Daisuke Takahashi for their help, and other people who related to this research. I am also grateful to Prof. Stephen G. Lambacher for correcting my English.