diff --git a/src/utils/find_longest_prefix_contained_within.rs b/src/utils/find_longest_prefix_contained_within.rs
index feff917..c167d3e 100644
--- a/src/utils/find_longest_prefix_contained_within.rs
+++ b/src/utils/find_longest_prefix_contained_within.rs
@@ -26,20 +26,50 @@ use crate::Token;
 /// new: [0, 4]
 /// ```
 /// > results in a range of 0..1
+///
+/// Runs in `O(old.len() + new.len())` using the Knuth-Morris-Pratt algorithm.
 pub fn find_longest_prefix_contained_within<T>(old: &[Token<T>], new: &[Token<T>]) -> Range<usize>
 where
     T: PartialEq + Clone + Debug,
 {
-    let max_possible = new.len().min(old.len());
+    if new.is_empty() {
+        return 0..0;
+    }
 
-    for len in (1..=max_possible).rev() {
-        let prefix = &new[..len];
-        if let Some(start) = old.windows(len).position(|window| window == prefix) {
-            return start..start + len;
+    // `fallback[i]` is the length of the longest proper prefix of `new[..=i]`
+    // that is also a suffix of it
+    let mut fallback = vec![0; new.len()];
+    let mut matched = 0;
+    for i in 1..new.len() {
+        while matched > 0 && new[i] != new[matched] {
+            matched = fallback[matched - 1];
+        }
+        if new[i] == new[matched] {
+            matched += 1;
+        }
+        fallback[i] = matched;
+    }
+
+    // `matched` is the longest prefix of `new` ending at the current token of
+    // `old`, so it first reaches its maximum at the earliest occurrence
+    let mut longest = 0..0;
+    matched = 0;
+    for (i, token) in old.iter().enumerate() {
+        while matched > 0 && *token != new[matched] {
+            matched = fallback[matched - 1];
+        }
+        if *token == new[matched] {
+            matched += 1;
+        }
+        if matched > longest.len() {
+            longest = i + 1 - matched..i + 1;
+            if matched == new.len() {
+                break;
+            }
         }
     }
 
-    0..0
+    longest
 }
 
 #[cfg(test)]
@@ -111,4 +141,42 @@ mod tests {
             0..0
         );
     }
+
+    #[test]
+    fn test_matches_brute_force_on_short_sequences() {
+        fn brute_force(old: &[Token<String>], new: &[Token<String>]) -> Range<usize> {
+            for len in (1..=new.len().min(old.len())).rev() {
+                if let Some(start) = old.windows(len).position(|window| window == &new[..len]) {
+                    return start..start + len;
+                }
+            }
+            0..0
+        }
+
+        let mut sequences: Vec<Vec<Token<String>>> = vec![Vec::new()];
+        let mut level = sequences.clone();
+        for _ in 0..5 {
+            level = level
+                .iter()
+                .flat_map(|sequence| {
+                    ["a", "b", "c"].map(|token| {
+                        let mut extended = sequence.clone();
+                        extended.push(token.into());
+                        extended
+                    })
+                })
+                .collect();
+            sequences.extend(level.iter().cloned());
+        }
+
+        for old in &sequences {
+            for new in &sequences {
+                assert_eq!(
+                    find_longest_prefix_contained_within(old, new),
+                    brute_force(old, new),
+                    "old={old:?}, new={new:?}"
+                );
+            }
+        }
+    }
 }