YOU SAID:

The cat thinks it is a dog pretending to be a cat, and the dog thinks it is a cat pretending to be a dog, and that is why the cat who is a dog chased the dog who is a cat.

INTO JAPANESE

猫はそれが猫であると思っている犬だと思っており、犬はそれが犬のような猫だと思っているので、犬である猫が猫である犬を追いかけたのです。

BACK INTO ENGLISH

The cat thinks that it is a dog who thinks it is a cat, and the dog thinks that it is a cat like a dog, so the cat who is a dog chase a dog that is a cat.

INTO JAPANESE

猫はそれが猫だと思っている犬だと思っており、犬はそれが犬のような猫だと思うので、犬である猫は猫である犬を追いかける。

BACK INTO ENGLISH

I think that a cat is a dog who thinks it is a cat, and a dog thinks that it is a cat like a dog, so a cat as a dog chases a dog that is a cat.

INTO JAPANESE

私は猫は猫だと思う犬だと思うし、犬はそれが犬のような猫だと思うので、犬のような猫は猫である犬を追いかける。

BACK INTO ENGLISH

I think that a cat is a dog who thinks it is a cat, and a dog thinks that it is a cat like a dog, so a cat like a dog chases a dog which is a cat.

INTO JAPANESE

私は猫は猫だと思う犬だと思うし、犬はそれが犬のような猫だと思うので、犬のような猫は猫である犬を追いかける。

BACK INTO ENGLISH

I think that a cat is a dog who thinks it is a cat, and a dog thinks that it is a cat like a dog, so a cat like a dog chases a dog which is a cat.