= Solution
The answer depends on the actual definitions above, especially the direction used for <duplicate removal>.
* `invert` works for an infinite <binary relation> enumerated by a <lazy list>: each output needs only one input pair, and swapping preserves distinctness.
* `removedup` is productive whenever the input has infinitely many distinct values and equality tests terminate. Each next new value occurs at a finite input position and passes finitely many earlier filters. In particular, it works on the stipulated distinct-element representation of an infinite <binary relation>. On an infinite <list> with only finitely many distinct values it emits those values but cannot certify that there is no next new value; for example, demanding the tail after the first result of `removedup (repeat 1)` diverges.
* `relcomp` does not work for arbitrary infinite inputs. Its nested <list comprehension> can remain forever in the inner generator. With `r = [(i,0) | i <- [0..]]` and `s = [(0,j) | j <- [0..]]`, it emits only pairs whose first component is zero, starving every later outer value. <Duplicate removal> cannot repair this lack of <fair enumeration>.
* `transclose` does not work for a general infinite input: even its first `length s` cannot finish. It waits for finite saturation before returning any result.
Thus $\boxed{\text{inversion works; deduplication has the stated productivity condition; composition and closure fail in general}}$. A fairer enumeration may improve the latter constructions, but would be a different <algorithm>; ordinary depth-first enumeration does not become fair through <lazy evaluation> alone.
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