  For Coxeter groups with sufficiently large braid relations, we prove that the
sequence of powers of a Coxeter element has unbounded reflection length. We
establish a connection between the reflection length functions on arbitrary
Coxeter groups and the reflection length functions on universal Coxeter groups
of the same rank through the solution to the word problem for Coxeter groups.
For Coxeter groups corresponding to a Coxeter matrix with the same entry
everywhere except the diagonal, upper bounds for the reflection length of the
powers of Coxeter elements are established.
