alienis cladibus

Inde contra Crustuminos bellum inferentes profectus est; ibi etiam minus certaminis fuit, quod alienis cladibus ceciderant animi hostium.

Romulus moves against the Crustumini ‘…ibi etiam minus certaminis fuit…’ and there there was a smaller army [smaller than the Amtenates who he has just defeated], …quod alienis cladibus cediderant animi hostium - because with the fall of the foreigners [alienis = Crustimini?] the spirits of the enemy had fallen…

So as I understand it:

“… and there was even less to fight (= your rendering keeps the spirit), because the minds of enemies had fallen (were already desperate) by means of/through different (other) losses/detriments/lost battles”

You can compare how same or different it is. Anything else or better wording is either matter of language or an added context that I lack.

“He set out from there making war against the Crustumini; in that place was even less of a struggle, because the courage of the enemy had failed due to the losses of the others…”

If context permitted it, “alienis cladibus” could also be rendered “losses determintal to them…”

Many thanks. Actually - to my embarrassment I was mistranslating certamen.