Amalgamated free product of Z and Z over 2Z

Definition as an amalgamated free product
The group is defined as the amalgamated free product $$\mathbb{Z} *_{2\mathbb{Z}} \mathbb{Z}$$, i.e., we take two copies of the group of integers, take their free product, and then take the quotient group by the identification of the subgroup $$2\mathbb{Z}$$.

Definition by presentation
The group can be defined by the presentation:

$$\langle x,y \mid x^2 = y^2 \rangle$$