diff --git a/core/trino-main/src/main/java/io/trino/sql/planner/NullabilityAnalyzer.java b/core/trino-main/src/main/java/io/trino/sql/planner/NullabilityAnalyzer.java
index 98dd6a49b6b8..dd503f403ea7 100644
--- a/core/trino-main/src/main/java/io/trino/sql/planner/NullabilityAnalyzer.java
+++ b/core/trino-main/src/main/java/io/trino/sql/planner/NullabilityAnalyzer.java
@@ -65,7 +65,7 @@ protected Void visitCast(Cast node, AtomicBoolean result)
             // except for the CAST(NULL AS x) case -- we should fix this at some point)
             //
             // Also, try_cast (i.e., safe cast) can return null
-            result.set(node.isSafe() || !node.isTypeOnly());
+            result.compareAndSet(false, node.isSafe() || !node.isTypeOnly());
             return null;
         }
 
diff --git a/core/trino-main/src/test/java/io/trino/sql/query/TestJoin.java b/core/trino-main/src/test/java/io/trino/sql/query/TestJoin.java
index ab7703176c0c..142432679919 100644
--- a/core/trino-main/src/test/java/io/trino/sql/query/TestJoin.java
+++ b/core/trino-main/src/test/java/io/trino/sql/query/TestJoin.java
@@ -77,6 +77,40 @@ public void testJoinOnNan()
                 .matches("VALUES (nan(), nan())");
     }
 
+    @Test
+    public void testJoinWithComplexCriteria()
+    {
+        // Test for https://github.com/trinodb/trino/issues/13145
+        // The issue happens because ReorderJoins evaluates candidates for equality inference
+        // based on one form of the join criteria (i.e., CAST(...) = CASE ... END)) and then
+        // attempts to make reformulate the join criteria based on another form of the expression
+        // with the terms flipped (i.e., CASE ... END = CAST(...)). Because NullabilityAnalyzer.mayReturnNullOnNonNullInput
+        // could return an inconsistent result for both forms, the expression ended being dropped
+        // from the join clause.
+        assertThat(assertions.query("" +
+                "WITH " +
+                "    t1 (id, v) as ( " +
+                "        VALUES " +
+                "            (1, 100), " +
+                "            (2, 200) " +
+                "    ), " +
+                "    t2 (id, x, y) AS ( " +
+                "        VALUES\n" +
+                "            (1, 10, 'a'), " +
+                "            (2, 10, 'b') " +
+                "    ), " +
+                "    t AS ( " +
+                "        SELECT " +
+                "            x " +
+                "            , IF(t1.v = 0, 'cc', y) as z " +
+                "        FROM t1 JOIN t2 ON (t1.id = t2.id) " +
+                "    ) " +
+                "SELECT * " +
+                "FROM t " +
+                "WHERE x = 10 AND z = 'b'"))
+                .matches("VALUES (10, CAST('b' AS varchar(2)))");
+    }
+
     @Test
     public void testInPredicateInJoinCriteria()
     {