= Strictly increasing subsequence
A <strictly increasing subsequence> selects indices $i_1<\cdots<i_m$ of a <sequence> with $x_{i_1}<\cdots<x_{i_m}$. Equal values cannot both occur in it. Its <maximum> possible length is $L_{<}(x)$, with $L_{<}(())=0$; in general $L_{<}(x)\leq L(x)$ for the weak <longest increasing subsequence>. Use strict comparisons in the <dynamic programming> <recurrence relation> and replace the first tail at least as large as the next value in the <binary search> <algorithm>.
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