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A blockchain, such as Bitcoin, is an append-only, secure, transparent, distributed ledger. A fair blockchain is expected to have healthy metrics; high honest mining power, low processing latency, i.e., low wait times for transactions and stable price of consumption, i.e., the minimum transaction fee required to have a transaction processed. As Bitcoin matures, the influx of transactions increases and the block rewards become insignificant. We show that under these conditions, it becomes hard to maintain the health of the blockchain. In Bitcoin, under these mature operating conditions (MOC), the miners would find it challenging to cover their mining costs as there would be no more revenue from merely mining a block. It may cause miners not to continue mining, threatening the blockchain's security. Further, as we show in this paper using simulations, the cost of acting in favor of the health of the blockchain, under MOC, is very high in Bitcoin, causing all miners to process transactions greedily. It leads to stranded transactions, i.e., transactions offering low transaction fees, experiencing unreasonably high processing latency. To make matters worse, a compounding effect of these stranded transactions is the rising price of consumption. Such phenomena not only induce unfairness as experienced by the miners and the users but also deteriorate the health of the blockchain. We propose BitcoinF transaction processing protocol, a simple, yet highly effective modification to the existing Bitcoin protocol to fix these issues of unfairness. BitcoinF resolves these issues of unfairness while preserving the ability of the users to express urgency and have their transactions prioritized.