After the germans were stopped at the first battle of the both sides dug in, and trench lines stretched from to the border of

After the Germans were stopped at the First Battle of the Marne, both sides dug in, and trench lines stretched from the North Sea to the border of Switzerland.

Explanation:

After the First Battle of the Marne and the German withdrawal to the Aisne, both sides began a series of maneuvers in which they tried to surpass the enemy from the north.

Initially the front ended at the Aisne River; it led the Germans to maneuver towards the allied side and occupy the positions at Chemin des Dames, on the western bank of the river. In turn, the allies flanked them from the west, to meet new German lines. The process was repeated until reaching the North Sea, with the battles of La Bassee, the First Battle of Ypres and Yser, at the end of October.

The result was a front line with continuous trenches in about 150 miles, which later extended to the entire western front line from the sea to the border with Switzerland.

This would end the war of movements and would give way to the so-called "trench war", which would predominate during the rest of the war.