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Dynamic algorithms come in three main flavors: $\mathit{incremental}$(insertions-only), $\mathit{decremental}$ (deletions-only), or $\mathit{fully}$$\mathit{dynamic}$ (both insertions and deletions). Fully dynamic is the holygrail of dynamic algorithm design; it is obviously more general than the othertwo, but is it strictly harder? Several works managed to reduce fully dynamicto the incremental or decremental models by taking advantage of either specificstructure of the incremental/decremental algorithms (e.g. [HK99, HLT01, BKS12,ADKKP16, BS80, OL81, OvL81]), or specific order of insertions/deletions (e.g.[AW14,HKNS15,KPP16]). Our goal in this work is to get a black-boxfully-to-incremental reduction that is as general as possible. We find that thefollowing conditions are necessary:  $\bullet$ The incremental algorithm must have a worst-case (rather thanamortized) running time guarantee.  $\bullet$ The reduction must work in what we call the$\mathit{deletions}$-$\mathit{look}$-$\mathit{ahead}$ $\mathit{model}$, wherethe order of deletions among current elements is known in advance. A notablepractical example is the "sliding window" (FIFO) order of updates.  Under those conditions, we design:  $\bullet$ A simple, practical, amortized-fully-dynamic toworst-case-incremental reduction with a $\log(T)$-factor overhead on therunning time, where $T$ is the total number of updates.  $\bullet$ A theoretical worst-case-fully-dynamic to worst-case-incrementalreduction with a $\mathsf{polylog}(T)$-factor overhead on the running time.

Fully-dynamic-to-incremental reductions with known deletion order (e.g. sliding window)