The time lower bounds for both uniform consensus and early stopping consensus have already been proved in synchronous distributed systems with crash failures, but both have not been proved with orderly crash failures and remain as open problems. This paper uses a bivalency argument proof to solve the two open problems. The first open problem is how to prove the lower bound, min (t + 1, f + 2) rounds, for early-stopping synchronous consensus with orderly crash failures, where t le n - 1 and 0 leqslant f leqslant t - 1. The second problem is to prove that the lower bound for early deciding uniform consensus with orderly crash failures is (f + 2)-rounds where 0 leqslant f leqslant t - 2, and (f + 1)-rounds when f = t and t -1.
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机译：两种统一共识和早期停止共识的时间下限已经在具有碰撞故障的同步分布式系统中证明，但两者都没有被证明有有序的崩溃失败，并仍然是公开问题。本文采用了一项双平凡的论点证明来解决两个打开问题。第一个开放问题是如何证明下限，最小（T + 1，F + 2）轮，用于重新停止具有有序碰撞故障的同步共识，其中T LE N-1和0 Leqslant F Leqslant T-1。第二个问题是为了证明具有有序碰撞故障的早期决定统一共识的下限是（f + 2） - 其中0 leqslant f Leqslant t-2，（f + 1） - 当f = t和t时舍出-1。
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