  In the paper, we establish Gr\"obner-Shirshov bases for semirings and
commutative semirings. As applications, we obtain Gr\"obner-Shirshov bases and
A. Blass's (1995) and M. Fiore -T. Leinster's (2004) normal forms of the
semirings $\mathbb{N}[x]/(x=1+x+x^2)$ and $\mathbb{N}[x]/(x=1+x^2)$ with one
generator $x$ and one defining relation, correspondingly.
