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Earlier studies used classical time series models to forecast the nonlinear connectedness of conventional crypto-assets with CO2 emissions. For the first time, this study aims to provide a data-driven Nonlinear System Identification technique to study the nonlinear connectedness of crypto-assets with CO2 emissions. Using daily data from January 2, 2019, to March 31, 2023, we investigate the nonlinear connectedness among conventional crypto-assets, sustainable crypto-assets, and CO2 emissions based on our proposed model, Multiple Inputs Single Output (MISO) Nonlinear Autoregressive with Exogenous Inputs (NARX). Intriguingly, the forecasting accuracy of the proposed model improves with the inclusion of exogenous input variables (conventional and sustainable crypto-assets). Overall, our results reveal that conventional crypto-assets exhibit slightly stronger connectedness with CO2 emissions compared to sustainable crypto-assets. These findings suggest that, to some extent, sustainable crypto-assets provide a solution to the environmental issues related to CO2 emissions. However, further improvements in sustainable crypto-assets through technological advances are required to develop more energy-efficient decentralised finance consensus algorithms, with the aim of reshaping the cryptocurrency ecosystem into an environmentally sustainable market.