I need to show that the following language is context free:

$$L = \{a^\ell b^n c^m | \ell, n, m \in \mathbb{N}^+ \wedge ((\ell \ge n) \vee (\ell \ge m))\}$$

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    $\begingroup$ Also asked at Math.SE. Please do not cross-post questions, especially ones that already have answers on another site. $\endgroup$ – Aaron Rotenberg 2 days ago

Hint 1: $L = L_1 \cup L_2$ for some $L_1$ and $L_2$ which are obviously context-free.

Hint 2:

$L_1 = \{a^\ell b^n c^m | \ell, n, m \in \mathbb{N}^+ \wedge (\ell \ge n)\}$


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