I've been given a solution, included below and I do not see how it would reject a string where i=j.
The example given should reject an input string such as
aabbcc where there are an equal number of a's an b's, so i=j, however I don't see how it would reject it. Wouldn't it just push 2 a's, transition to state 2, pop 2 a's, epsilon transition to state 4, read in the two c's without popping or pushing and then accept? Is the given solution wrong or am I missing something?