  We introduce a reduction order called the weighted path order (WPO) that
subsumes many existing reduction orders. WPO compares weights of terms as in
the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide
class of interpretations. We investigate summations, polynomials and maximums
for such interpretations. We show that KBO is a restricted case of WPO induced
by summations, the polynomial order (POLO) is subsumed by WPO induced by
polynomials, and the lexicographic path order (LPO) is a restricted case of WPO
induced by maximums. By combining these interpretations, we obtain an instance
of WPO that unifies KBO, LPO and POLO. In order to fit WPO in the modern
dependency pair framework, we further provide a reduction pair based on WPO and
partial statuses. As a reduction pair, WPO also subsumes matrix
interpretations. We finally present SMT encodings of our techniques, and
demonstrate the significance of our work through experiments.
