Here are the equations.

  1. largestCommonPrefix(x::xs, x::ys) = x::largestCommonPrefix(xs, ys)
  2. largestCommonPrefix(x,y)          = []

Here is an inside-out evaluation of largestCommonPrefix([2,5,3,9,5], [2,5,2,9,5]).

  largestCommonPrefix([2,5,3,9,5], [2,5,2,9,5])
    = 2::largestCommonPrefix([5,3,9,5], [5,2,9,5])   (by eq. 1)
    = 2::5::largestCommonPrefix([3,9,5], [2,9,5])    (by eq. 1)
    = 2::5::[]                                       (by eq. 2)