The Complexity of The Collection of Countable Linear Orders of The Form I + I

0. Abstract First we prove that the set of countable linear orders of the form I +I form a complete analytic set. As a consequence of this we improve a result of Humke and Laczkovich, who showed in HL] that the set of functions of the form f f form a true analytic set in C0; 1]. We show that these functions form a complete analytic set, solving a problem mentioned on p.215 of K] and on p.4 of B].