καταπολεμ-έω · katapolem-eō — LSJ
war down, i.e. exhaust by war, reduce, τὴν Πελοπόννησον Th. 2.7, cf. 4.1, And. 3.15, X. HG 7.1.10: pres., attempt to subdue, ἐγκλήμασι Th. 4.86:—Pass., ἐλπίζοντες αὐτὴν [τὴν πόλιν] καταπεπολεμῆσθαι Id. 6.16, cf. Pl. Mx. 243c, 243d.
simply, make war against, τινα Phld. Piet. 54: abs., carry on warfare, τοῖς ὅλοις Plu. Caes. 26.