Electrolysis of water is the decomposition reaction, because from one molecule (water) two molecules (hydrogen and oxygen) are produced. Water is separeted into two molecules:
Reaction of reduction at cathode: 2H⁺(aq) + 2e⁻ → H₂(g).
Reaction of oxidation at anode: 2H₂O(l) → O₂(g) + 4H⁺(aq) + 4e⁻.