Songs on Nataraja

[HarishankarK]

Who composed first?
Tyagarajar Rama Nee samaanamevaru or
GKB Sabapathikku?
Here in one of the posts it's says Tyagarajar response to GKB was Rama Nee Samana
Is that even remotely correct?

[P. S.]

Sundara Natarajam - Kharaharapriya - Adi - Ootukadu

Sri Pulliyur Duraiswami Iyer was a great devotee of Nataraja and composed many songs in Telugu and Sanskrit. Of these songs, I have only been able to find Durjati and Adenamma
Thatta Dhimita - Todi - Rupakam
Parahamsa Nalona Palimpave - Ahiri - Jhampa
Parama Sadashiva - Bowli - Adi
Durjati - Gowri - Adi
Adenamma - Pharaju - Adi
Mandugai konare - Saveri - Adi
Pashupati I hrdaya - Yadukula Kambhoji - Khanda Chapu
Elagu Daya - Shankarabharanam - Misra Chapu
Adbhuta Natanam - Pantuvarali - Misra Chapu