  The relative index theorem is proved for general first-order elliptic
operators that are complete and coercive at infinity over measured manifolds.
This extends the original result by Gromov-Lawson for generalised Dirac
operators as well as the result of B\"ar-Ballmann for Dirac-type operators. The
theorem is seen through the point of view of boundary value problems, using the
graphical decomposition of elliptically regular boundary conditions for general
first-order elliptic operators due to B\"ar-Bandara. Splitting, decomposition
and the Phi-relative index theorem are proved on route to the relative index
theorem.
