Absurd Brainfuck

Absurd Brainfuck is a Brainfuck-derivative by Tailcalled. It is called 'absurd' because the side effects flow in the opposite direction of the data. In other words, when you change a cell, you change what it *was*, not what it is. This can lead to undecidable scenarios, of course.

Commands
Absurd Brainfuck has the commands of Brainfuck, but with a "slightly" different effect.

+   Changes the current cell to be one higher in the past -   Changes the current cell to be one lower in the past >   Goes to the next cell in the past <   Goes to the previous cell in the past .   Outputs the current value of the current cell. ,   Reads a value and puts it in the current cell in the past. [p] Executes p until the value of the current cell is 0.

Memory
Absurd Brainfuck has an infinite tape in *both* directions.

Computational Class
It is unknown how powerful Absurd Brainfuck is.