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 $L_{<}(x)\le L(x)$ 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.