The degree of nonminimality is at most two
Abstract : It is shown that if \( p \) is a complete type of Lascar rank at least 2 over \( A \), in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations, \( a_1 \) and \( a_2 \), such that \( p \) has a nonalgebraic forking extension over \( A,a_1,a_2 \). Moreover, if A is contained in the field of constants then \( p \) already has a nonalgebraic forking extension over \( A,a_1 \). The results are also formulated in a more general setting.