  We study the system of double Rashba wires brought into the proximity to an
$s$-wave superconductor. The time reversal invariant topological
superconductivity is realized if the interwire pairing corresponding to crossed
Andreev reflection dominates over the standard intrawire pairing. We derive the
topological criterion and show that the system hosts zero energy Andreev bound
states such as a Kramers pair of Majorana fermions. We classify symmetry of the
Cooper pairs focusing on the four degrees of freedom, $i.e.$, frequency, spin,
spatial parity inside wires, and spatial parity between wires. The magnitude of
the odd-frequency pairing is strongly enhanced in the topological state. We
also explore properties of junctions occurring in such double wire systems. If
one section of the junction is in the topological state and the other is in the
trivial state, the energy dispersion of Andreev bound states is proportional to
$\sim\pm\sin\varphi$, where $\varphi$ denotes the macroscopic phase difference
between two sections. This behavior can be intuitively explained by the
couplings of a Kramers pair of Majorana fermions and spin-singlet $s$-wave
Cooper pair and can also be understood by analyzing an effective continuum
model of the $s+p$/$s$-wave superconductor hybrid system.
