  In this paper we wish to find the corresponding Gibbons-Hawking-York term for
the most general quadratic in curvature gravity by using Coframe slicing within
the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions.
In order to make sure that the higher derivative gravity is ghost and tachyon
free at a perturbative level, one requires infinite covariant derivatives,
which yields a generalised covariant infinite derivative theory of gravity. We
will be exploring the boundary term for such a covariant infinite derivative
theory of gravity.
