From e8443cd07126425aad3f97fd734582e48e4bf712 Mon Sep 17 00:00:00 2001
From: Snaipe <franklinmathieu@gmail.com>
Date: Sun, 3 May 2015 16:19:23 +0200
Subject: [PATCH] Fixed wrong step in max_length proof

---
 src/extmatch.c | 25 +++++++++++++++----------
 1 file changed, 15 insertions(+), 10 deletions(-)

diff --git a/src/extmatch.c b/src/extmatch.c
index 486a612..f03154d 100644
--- a/src/extmatch.c
+++ b/src/extmatch.c
@@ -218,21 +218,26 @@ static int transform(const char *pattern, char *result, const char **errmsg) {
  * We must now find the maximal length L such as ∀s, L >= length(T(s))
  *
  * It is immediately apparent that the largest string will depend on the number
- * of occurrences of '!()'. Hence, let s be a string that is a repeating
- * sequence of '!()',
+ * of occurrences of '!()'. Hence, let u be a string that is a repeating
+ * sequence of '!()' padded by '.' to a multiple of 3,
  *
- * let N = floor(length(s) / 3),
- * let Q = length(s) mod 3,
- * ∀s, num('!()') = N (1)
+ * let N = floor(length(u) / 3),
+ * let Q = length(u) mod 3,
+ * hence num('!()') = N.
  *
- * ∀s, length(T(s)) <= length(s) + 4 * N
- *                  <= 3 * N + Q + 4 * N
- *                  <= 7 * N + 2
- *                  <= 7 * floor(length(s) / 3) + 2
+ * ∀s | lenght(s) = length(u),
+ *     length(T(s)) <= length(T(u))
+ *                  <= length(u)            | the original length
+ *                      + 4 * N             | the expansion of all '!()'
+ *                      + Q * diff('.')     | the expansion of Q '.'
+ *                  <= 3 * N + Q + 4 * N + Q
+ *                  <= 7 * N + 4
+ *                  <= 7 * floor(length(u) / 3) + 4
+ *                  <= 7 * floor(length(s) / 3) + 4
  *
  */
 static inline size_t max_length(size_t len) {
-    return 7 * len / 3 + 2;
+    return 7 * len / 3 + 4;
 }
 
 int extmatch(const char *pattern, const char *string, const char **errmsg) {