  We implement a decision procedure for answering questions about a class of
infinite words that might be called (for lack of a better name)
"Fibonacci-automatic". This class includes, for example, the famous Fibonacci
word f = 01001010..., the fixed point of the morphism 0 -> 01 and 1 -> 0. We
then recover many results about the Fibonacci word from the literature (and
improve some of them), such as assertions about the occurrences in f of
squares, cubes, palindromes, and so forth. As an application of our method we
prove a new result: there exists an aperiodic infinite binary word avoiding the
pattern x x x^R. This is the first avoidability result concerning a nonuniform
morphism proven purely mechanically.
