Deforestation

Two players take turns cutting leaves from a rooted tree with n nodes numbered from 0 to n-1, rooted at node 0. On each turn, a player selects a leaf — a non-root node with no children in the remaining tree — and removes it along with its incident edge. As leaves are removed, formerly internal nodes become new leaves once all their children are gone. The root is never removed. The player who cannot move (because no non-root leaves remain) loses. Both players play optimally. Determine whether the first player can force a win.

Examples
Input: [3,[[0,1],[1,2]]]
Output: false
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Deforestation

Two players take turns cutting leaves from a rooted tree with n nodes numbered from 0 to n-1, rooted at node 0. On each turn, a player selects a leaf — a non-root node with no children in the remaining tree — and removes it along with its incident edge. As leaves are removed, formerly internal nodes become new leaves once all their children are gone. The root is never removed. The player who cannot move (because no non-root leaves remain) loses. Both players play optimally. Determine whether the first player can force a win.