algebraic notation is broken
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1.a4 Nh6 2.b4 Ng8 3.b5 Nh6 4.a5 Ng8 5.b6 Nh6 6.a6 Ng8 7.axb7 Nh6 8.bxa7 Ng8 9.bxa8=Q Nh6 10.axb8=Q Ng8 11.Qb6 Nh6 12.Qaa5 Ng8 13.c4 Nh6 14.Qda4 Ng8 15.Qab5 Nh6 16.Q6a6 Ng8 17.Qab6 Nh6 18.c5 Ng8 19.c6 Nf6 20.e4 Nd5 21.exd5 Rg8 22.d6 Rh8 23.dxc7 Rg8 24.d3 f6 25.cxd8=Q+ Kf7 26.Qdc7 Ke6 27.Qca7 Kf7 28.Qac7 d6 29.Qca7 d5 30.Qba6
This is prof that algebraic notation is broken
Well, it's not the algebra part that is "broken". It's only that the short algebraic notation is not suitable for this case but the long algebraic notation will do fine. There are instances where even the long notation does not suffice especially related to reversed moves. When somebody asks you what the last move in a position was, the answer Rf4xf6 will not tell anyone what unit was captured. Reversible notations enable you to play any move in forward and in backward direction.