The word position automaton was introduced by Glushkov and McNaughton in the early 1960. This automaton is homogeneous and has (||E|| + 1) states for an expression of alphabetic width ||E||. In this paper this type of automata is extended to regular tree expressions and it is shown that the conversion of a regular tree expression of size |E| and alphabetic width ||E|| into its reduced tree automaton can be done in
(|E|·||E||) time. The time complexity of the algorithm proposed by Dietrich Kuske and Ingmar Meinecke is also proved in order to reach an
(||E||·|E|) time complexity for the problem of the construction of the equation automaton from a regular tree expression.