  We propose a new order, the small polynomial path order (sPOP* for short).
The order sPOP* provides a characterisation of the class of polynomial time
computable function via term rewrite systems. Any polynomial time computable
function gives rise to a rewrite system that is compatible with sPOP*. On the
other hand any function defined by a rewrite system compatible with sPOP* is
polynomial time computable. Technically sPOP* is a tamed recursive path order
with product status. Its distinctive feature is the precise control provided.
For any rewrite system that is compatible with sPOP* that makes use of
recursion up to depth d, the (innermost) runtime complexity is bounded from
above by a polynomial of degree d.
