Is there any such thing as a decidable problem that cannot be bounded in complexity by a function?
Let L be the language of pairs of computable expressions/programs that would evaluate to the same value.
Can this language be bounded? If the expressions are provably halting than the language must be decidable but the time to decide would seem to be arbitrarily large.
The problem you mention is not, in fact, decidable: there is no algorithm to decide if $\Phi_d(a)\cong\Phi_e(b)$ (where $\Phi_i(n)$ denotes the $i$th Turing machine run on input $n$, and $\cong$ is the standard notion of equality between possibly undefined values - either both sides are undefined, or both sides are defined and equal). This is a good exercise.
And it doesn't help to restrict attention to the provably halting expressions: the set of such expressions is undecidable! (It is recursively enumerable, but not co-recursively enumerable.)
In fact, by definition any decidable problem is time-bounded by a computable function - a problem is decidable if there is a total Turing machine $\Phi_e$ which decides it, and the runtime of a total Turing machine is a total computable function (exercise).
