x_{1} and x_{2} are path-linked by binary predicate x_{3} (ka; possibly non-symmetric/non-commutative) via some from-x_{1}-to-x_{2}-directed path of length x_{4} (li; nonnegative integer or positive infinity) in/through graph x_{5} (default: maximal) which is generated by relation x_{3}.

Like ".utka'au" but primarily without the constraint that a geodesic path be chosen. The requirement simply is that there exists at least one path from x_{1} to x_{2} via steps related by x_{3} in x_{5} such that the path has total length x_{4}. Notice that this does not interact well if the directed graph is connected to at least one cycle. Otherwise, as appropriate, this word and all of its notes are equivalent to those of ".utka'au".

- utka'au
- x
_{1}and x_{2}are path-linked by binary predicate x_{3}(ka; possibly non-symmetric/non-commutative) via a from-x_{1}-to-x_{2}-directed graph geodesic of length x_{4}(li; nonnegative integer or positive infinity) in graph x_{5}(default: maximal) which is generated by relation x_{3}.