The defining feature of Tier 1 has always been power, not popularity. At the time that FAQ entry was written, the two statements were equivalent.
Let me rephrase my second comment:
TADS, Inform, and Hugo started with a Turing-complete core, then designed the rest of the language around that core. All features of the language can be accessed from that core.
ADRIFT appears to have been designed at the UI-level, with Turing-completeness being only an afterthought. (And I'm not sure whether ADRIFT is Turing-complete; I don't think it's possible to write programs that take arbitrarily long to run; I don't think it has looping constructs, and recursion can lead to stack overflow.)
To show a language is TC, write any TC problem within your language. (Writing a Brainf___ interpreter in a language is a popular one, with BF being a fairly simple language. (Simple from the POV of a person trying to make a BF compiler / interpreter. Not simple from the POV of a person trying to do anything in BF.))
- Should be able to run an arbitrary BF program on arbitrary input. (Exact mechanism for entering a program and input are up to you. For example, you might have the user open the program in Developer, put the program and input into various strings, then start the program in runner).
- Should be able to run programs that take arbitrarily long to run.
- Behavior on edge cases (reading a "<" at memory location 0, reading a ">" at the greatest memory location, programs where brackets aren't balanced) is implementation defined. Do whatever's convenient. (Most of the complexity of my BF extension was handling those cases nicely.)
(BF extension and samples for I7. Was written quickly, may be rough around edges)
Bloodhounds can make you laugh and cuss in the same breath. They are endearing, faithful, and can sling drool ten feet in any direction. -- Virginia Lanier