To what extent do you think that Frederick Barbarossa's death contributed to the failure of the Third Crudade in 1190?

I believe that his death was the single largest factor leading to the eventual failure of the third crusade. The subsequent dissolusion of his 20,000 strong army following his death meant that King Richard of England and King Philip of France were greatly disadvantaged. But despite this unfortunate setback to the armies of christendom, they managed to achive a magnanimous victory at Arsuf! do you perhaps believe that Richard the 'Lionhearted' had the power to fulfil the aims of the crusade? or that he couldn't because of lack of man-power? - linking back to the original question.

Any opinions or thoughts will be greatly appreciated.

Thanks