TPiS (Total Procedures in Scheme) is a static analyzer, written in Scheme, which can check if given Scheme procedures are total (i.e. always terminate, on any input) by checking that they are specified primitive-recursively.
What's more, it is written almost entirely in a primitive-recursive style, so it can pass its own checks!
(There is one small Mulligan it must take, which is that it must guard itself against its caller passing it a cyclic list, and it can't detect that the code that implements this guard is total. This would be a non-issue in a purely functional dialect of Scheme where there were no such lists.)