Step 1: Recall the strange behaviour Belady's anomaly describes.
Normally, giving a process more page frames should reduce or at worst keep the same number of page faults. Belady's anomaly is the surprising exception where adding more frames actually increases the page fault count.
Step 2: See why FIFO is vulnerable to this.
FIFO simply evicts whichever page has been sitting in memory the longest, with no regard to how often or how recently it has actually been used. With more frames, the specific sequence of arrivals and evictions can shift in a way that removes a page just before it was about to be reused again, which is exactly the counter intuitive pattern that causes extra faults.
Step 3: Compare with the well behaved algorithms.
Optimal replacement always evicts the page that will not be needed for the longest time in the future, and LRU evicts based on actual recent usage, both belong to a class of stack based algorithms that are mathematically proven never to suffer from this anomaly. LFU also tracks usage frequency rather than mere arrival order, so it too avoids the classic problem associated with FIFO.
Step 4: Conclude.
The algorithm historically and classically shown to exhibit Belady's anomaly is
\[ \boxed{\text{FIFO}} \]