Can Non-termination be considered an algebraic effect? Non-termination is sometimes considered an effect.  I have been reading about algebraic effect systems (What is algebraic about algebraic effects and handlers?), and I suspect non-termination (like that arising from a fixed point operator) could fit in the algebraic effect framework.

For instance if effects systems act like continuations, it seems easy to add a handler that supplies "fuel" for possibly non-terminating computations.

Another way to encode a non-termination effect might be though SKI combinators, since they are Turing complete and I think they can be presented as an algebra.

The programing language Koka has a non-termination effect, but it is a built in "primitive" effect.  So it's unclear to me if it could be encoded by a user in their standard effect system.

Can non-terminating computation be considered an algebraic effect?  If so, are there standard ways to do it?  Any references would be great.
Non-termination can be considered an algebraic effect up to a point. It's an exception that cannot be handled. More precisely, we may introduce a nullary operation (constant) $\bot$ which signifies non-termination, but then we disallow handling it, as that would allow us to implement the Halting oracle.

Such treatment of non-termination is a bit naive. A more satisfactory account of non-termination would use domain-theoretic semantics, or a lifting monad.