What is the ruling when the claimed amount by the owner is higher than the animal's value, or the claimed rent exceeds the animal's value, and the parties dispute the contract type accordingly?

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If the owner claims the animal was a loan for use to claim its full value (which is higher than any potential rent) while denying the rent is due, and the rider claims it was leased, or if the owner claims the higher rent, and the rider claims it was a loan for use, the owner's statement prevails in both scenarios. Upon swearing, the owner is entitled to what they swore to. The position of Al-Shafi'i regarding all these matters aligns with what has been detailed.