  The impacts of the carrier-envelope phase (CEP) of a long relativistic
tightly-focused laser pulse on the dynamics of a counter-propagating electron
beam have been investigated in the, so-called, electron reflection regime,
requiring the Lorentz factor of the electron $\gamma$ to be approximately two
orders of magnitudes lower than the dimensionless laser field parameter $\xi$.
The electrons are reflected at the rising edge of the laser pulse due to the
ponderomotive force of the focused laser beam, and an asymmetric electron
angular distribution emerges along the laser polarization direction, which
sensitively depends on the CEP of the driving laser pulse for weak radiative
stochastic effects. The CEP siganatures are observable at laser intensities of
the order or larger than $10^{19}$ W/cm$^2$ and the pulse duration up to 10
cycles. The CEP detection resolution is proportional to the electron beam
density and can achieve approximately $0.1^{\circ}$ at an electron density of
about $10^{15}$ cm$^{-3}$. The method is applicable for currently available
ultraintense laser facilities with the laser peak power from tens of terawatt
to multi-petawatt region.
