diff --git a/gcc/testsuite/gcc.dg/strcmpopt_12.c b/gcc/testsuite/gcc.dg/strcmpopt_12.c
new file mode 100644
index 00000000000..d8077b62f7f
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/strcmpopt_12.c
@@ -0,0 +1,17 @@
+/* PR tree-optimization/96758 */
+/* { dg-do run } */
+/* { dg-options "-O2" } */
+
+int v = 1;
+
+int
+main ()
+{
+  const char *s = v ? "a" : "b";
+  char x[5];
+  char y[5] = "a\0a";
+  __builtin_memcpy (x, y, sizeof (y));
+  if (__builtin_strncmp (x, s, 4) != 0)
+    __builtin_abort ();
+  return 0;
+}
diff --git a/gcc/tree-ssa-strlen.c b/gcc/tree-ssa-strlen.c
index fbaee745f7d..96962286735 100644
--- a/gcc/tree-ssa-strlen.c
+++ b/gcc/tree-ssa-strlen.c
@@ -4485,11 +4485,19 @@ handle_builtin_string_cmp (gimple_stmt_iterator *gsi, const vr_values *rvals)
     ++cstlen2;
 
   /* The exact number of characters to compare.  */
-  HOST_WIDE_INT cmpsiz = bound < 0 ? cstlen1 < 0 ? cstlen2 : cstlen1 : bound;
+  HOST_WIDE_INT cmpsiz;
+  if (cstlen1 >= 0 && cstlen2 >= 0)
+    cmpsiz = MIN (cstlen1, cstlen2);
+  else if (cstlen1 >= 0)
+    cmpsiz = cstlen1;
+  else
+    cmpsiz = cstlen2;
+  if (bound >= 0)
+    cmpsiz = MIN (cmpsiz, bound);
   /* The size of the array in which the unknown string is stored.  */
   HOST_WIDE_INT varsiz = arysiz1 < 0 ? arysiz2 : arysiz1;
 
-  if (cmpsiz < varsiz && used_only_for_zero_equality (lhs))
+  if ((varsiz < 0 || cmpsiz < varsiz) && used_only_for_zero_equality (lhs))
     {
       /* If the known length is less than the size of the other array
 	 and the strcmp result is only used to test equality to zero,