Nonelementary problem

In computational complexity theory, a nonelementary problem is a problem that is not a member of the class ELEMENTARY. As a class it is sometimes denoted as NONELEMENTARY.

Examples of nonelementary problems that are nevertheless decidable include:
 * the problem of regular expression equivalence with complementation
 * the decision problem for monadic second-order logic over trees (see S2S)
 * the decision problem for term algebras
 * satisfiability of W. V. O. Quine's fluted fragment of first-order logic
 * deciding β-convertibility of two closed terms in typed lambda calculus
 * reachability in vector addition systems; it is Ackermann-complete.
 * reachability in Petri nets; it is Ackermann-complete.