  The fully anisotropic two-leg spin-1/2 $XXZ$ ladder model is studied in terms
of an algorithm based on the tensor network representation of quantum many-body
states as an adaptation of projected entangled pair states to the geometry of
translationally invariant infinite-size quantum spin ladders. The tensor
network algorithm provides an effective method to generate the groundstate wave
function, which allows computation of the groundstate fidelity per lattice
site, a universal marker to detect phase transitions in quantum many-body
systems. The groundstate fidelity is used in conjunction with local order and
string order parameters to systematically map out the groundstate phase diagram
of the ladder model. The phase diagram exhibits a rich diversity of quantum
phases. These are the ferromagnetic, stripe ferromagnetic, rung singlet, rung
triplet, N$\rm \acute{e}$el, stripe N$\rm \acute{e}$el and Haldane phases,
along with the two $XY$ phases $XY1$ and $XY2$.
