  Being a fully automated technique for resource analysis, automatic amortized
resource analysis (AARA) can fail in returning worst-case cost bounds of
programs, fundamentally due to the undecidability of resource analysis. For
programmers who are unfamiliar with the technical details of AARA, it is
difficult to predict whether a program can be successfully analyzed in AARA.
Motivated by this problem, this article identifies classes of programs that can
be analyzed in type-based polynomial AARA. Firstly, it is shown that the set of
functions that are typable in univariate polynomial AARA coincides with the
complexity class PTIME. Secondly, the article presents a sufficient condition
for typability that axiomatically requires every sub-expression of a given
program to be polynomial-time. It is proved that this condition implies
typability in multivariate polynomial AARA under some syntactic restrictions.
