Recursion schemes and recursive programs are exponentially hard to analyze

Deterministic exponential lower time bounds are presented for analyzing recursion schemes and recursive programs. The lower bounds for recursion schemes hold for any interpretation with a nontrivial predicate, i.e. a predicate that is neither identically true nor identically false. The lower bounds for recursive programs hold for very simple programs in any recursive programming language with a nontrivial predicate. These lower time bounds hold for the executability, computational identity, totality, divergence, partial correctness, and total correctness problems.