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(Visualizing the structure)
Consider nodes 1 through 6 where f(1)=2, f(2)=3, f(3)=4, f(4)=3, f(5)=6, f(6)=6. Each node has exactly one outgoing edge. From node 1: you go 1→2→3→4→3→4→… The tail is 1→2, and the cycle is 3→4→3.
The tail has length 2, the cycle has length 2. From node 6: you stay at 6 forever. A self-loop is a cycle of length 1. Every node eventually reaches a cycle, possibly immediately.
