## Proof (by contradiction)
Assume GOOD-TM is regular.
Then exists a FA with N states which accepts
for w with more than N lettters
there exists strings x, y ≠ ε, and z s.t.
– w = xyz
– length(x) + length(y) ≤ N
– xyz, xyyz, .. , x$y^n$z are words in GOOD-TM
Because y repeating many times, if $y^i$ contains one row in TM, then $y^{2i}$ will have two same rows,
which is invalid and not GOOD-TM. Thus, it is a contradiction.