Let $x=(a,b)$, where $a,b$ are in $N$
Now we have the transformations: $$T_1(x) = (ka, b+1)$$ $$T_2(x) = (b,a)$$ where $k$ is in $N$. Where the order of choosing a transformation is not fixed. (E.g. you can first apply 3 times $$T_1(x)$$, then $$T_2(x)$$
Will we for all $(a,b)$ produce $a=b$ by only being allowed to use these two transformations? If so, is this true for every $k$? I'm specifically interested in the case $k=2$ though.