  Cosmic shear statistics, such as the two-point correlation function (2PCF),
can be evaluated with the PDF-SYM method instead of the traditional
weighted-sum approach. It makes use of the full PDF information of the shear
estimators, and does not require weightings on the shear estimators, which can
in principle introduce additional systematic biases. This work presents our
constraints on $S_8$ and $\Omega_m$ from the shear-shear correlations using the
PDF-SYM method. The data we use is from the z-band images of the Dark Energy
Camera Legacy Survey (DECaLS), which covers about 10000 deg$^2$ with more than
100 million galaxies. The shear catalog is produced by the Fourier\_Quad
method, and well tested on the real data itself with the field-distortion
effect. Our main approach is called quasi-2D as we do use the photo-$z$
information of each individual galaxy, but without dividing the galaxies into
redshift bins. We mainly use galaxy pairs within the redshift interval between
0.2 and 1.3, and the angular range from $4.7$ to $180$ arcmin. Our analysis
yields $S_8=0.762 \pm 0.026$ and $\Omega_{\rm m}=0.234 \pm 0.075$, with the
baryon effects and the intrinsic alignments included. The results are robust
against redshift uncertainties. We check the consistency of our results by
deriving the cosmological constraints from auto-correlations of $\gamma_1$ and
$\gamma_2$ separately, and find that they are consistent with each other, but
the constraints from the $\gamma_1$ component is much weaker than that from
$\gamma_2$. It implies a much worse data quality of $\gamma_1$, which is likely
due to additional shear uncertainties caused by CCD electronics (according to
the survey strategy of DECaLS). We also perform a pure 2D analysis, which gives
$S_8=0.81^{+0.03}_{-0.04}$ and $\Omega_{\rm m}=0.25^{+0.06}_{-0.05}$. Our
findings demonstrate the potential of the PDF-SYM method for precision
cosmology.
