Fly does substitutions, but that's it: no loops, no if-thens. It's almost certain that something can be tickled into being Turing-complete; it's actually devilishly difficult to avoid doing it by accident. My hunch is pipelines are Turing complete, but I haven't gotten around to proving it.

But there's a difference between trying not to introduce it and going out of your way to build a programming language in YAML. An actual, honest-to-god programmable YAML.