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Οurous
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Haskell, 47 40 bytes

-7 thanks to OMᗺ

f b|(u,v)<-span('/'<)b="/1"++('0'<$u)==v

Try it online!

A port of my Clean answer using Neil's method.

Οurous
  • 8.1k
  • 1
  • 16
  • 38