Language of walks in a grid – context-free?
If your language $L$ were context-free then so would $L \cap u^* l^* d^* r^*$ be. However, $L \cap u^* l^* d^* r^* = \{ u^n l^m d^n r^m : n,m \geq 0 \}$, which is known not to be context-free (this can be proved using the pumping lemma).