In order to attain the requisite sensitivity for LISA - a joint space mission
of the ESA and NASA- the laser frequency noise must be suppressed below the
secondary noises such as the optical path noise, acceleration noise etc. By
combining six appropriately time-delayed data streams containing fractional
Doppler shifts - a technique called time delay interferometry (TDI) - the laser
frequency noise may be adequately suppressed. We consider the general model of
LISA where the armlengths vary with time, so that second generation TDI are
relevant. However, we must envisage the possibility, that not all the optical
links of LISA will be operating at all times, and therefore, we here consider
the case of LISA operating with two arms only. As shown earlier in the
literature, obtaining even approximate solutions of TDI to the general problem
is very difficult. Since here only four optical links are relevant, the
algebraic problem simplifies considerably. We are then able to exhibit a large
number of solutions (from mathematical point of view an infinite number) and
further present an algorithm to generate these solutions