David Gajser: Verifying time complexity of Turing machines

Two people, Andrej and Tomaž, have their own one-tape Turing machine. Andrej asserts, that his TM runs in time A(n) and Tomaž asserts that his TM runs in time T(n). Suppose A(n)=o(n log(n)) and T(n)=\Omega(n log(n)). We claim that Tomaž is able to verify Andrej's assertion, but Andrej has no algorithm to verify the assertion of Tomaž.