This is one of a series of papers in which the author applies the standard methods in modal logic to solve some problems on dynamic logic [cf. Stud. Logica 39, 275-295 (1980; Zbl 0457.03014) and Universal algebra and applications, Semester 1978, Banach Center Publ. 9, 31-46 (1982; Zbl 0546.03011)]. The completeness of the (smallest) total dynamic logic is proved by the canonical model/filtration technique. The finite model property and decidability are also obtained as by-products.