Coin flips moving two numbers together

High school · ●●●○○ 50 pts

Steph and Jeff each start with the number 4, and Travis is flipping a coin. Every time he flips heads, Steph replaces her number

x

with

2x-1

, and Jeff replaces his number

y

with

y+8

. Every time he flips tails, Steph replaces her number

x

with

\frac{x+1}{2}

, and Jeff replaces his number

y

with

y-3

. After some (positive) number of coin flips, Steph and Jeff end up with the same number, which is below 2012. How many times was the coin flipped?