diff --git a/expander_compiler/src/circuit/ir/source/chains.rs b/expander_compiler/src/circuit/ir/source/chains.rs
index d90af87..64ed3b7 100644
--- a/expander_compiler/src/circuit/ir/source/chains.rs
+++ b/expander_compiler/src/circuit/ir/source/chains.rs
@@ -140,6 +140,7 @@ impl<C: Config> Circuit<C> {
 }
 
 impl<C: Config> RootCircuit<C> {
+    // this function must be used with remove_unreachable
     pub fn detect_chains(&mut self) {
         for (_, circuit) in self.circuits.iter_mut() {
             circuit.detect_chains();
diff --git a/expander_compiler/src/circuit/ir/source/tests.rs b/expander_compiler/src/circuit/ir/source/tests.rs
index e4f7e08..7b789b3 100644
--- a/expander_compiler/src/circuit/ir/source/tests.rs
+++ b/expander_compiler/src/circuit/ir/source/tests.rs
@@ -1,7 +1,7 @@
 use rand::{Rng, RngCore};
 
 use super::{
-    ConstraintType,
+    Circuit, ConstraintType,
     Instruction::{self, ConstantLike, LinComb, Mul},
     RootCircuit,
 };
@@ -190,3 +190,75 @@ fn opt_remove_unreachable_2() {
         }
     }
 }
+
+fn test_detect_chains_inner(is_mul: bool, seq_typ: usize) {
+    let n = 1000000;
+    let mut root = RootCircuit::<C>::default();
+    let mut insns = vec![];
+    let mut lst = 1;
+    let get_insn = if is_mul {
+        |x, y| Instruction::<C>::Mul(vec![x, y])
+    } else {
+        |x, y| {
+            Instruction::LinComb(expr::LinComb {
+                terms: vec![
+                    expr::LinCombTerm {
+                        coef: CField::one(),
+                        var: x,
+                    },
+                    expr::LinCombTerm {
+                        coef: CField::one(),
+                        var: y,
+                    },
+                ],
+                constant: CField::zero(),
+            })
+        }
+    };
+    if seq_typ == 1 {
+        lst = n;
+        for i in (1..n).rev() {
+            insns.push(get_insn(lst, i));
+            lst = n * 2 - i;
+        }
+    } else if seq_typ == 2 {
+        for i in 2..=n {
+            insns.push(get_insn(lst, i));
+            lst = n - 1 + i;
+        }
+    } else {
+        let mut q: Vec<usize> = (1..=n).collect();
+        let mut i = 0;
+        lst = n;
+        while i + 1 < q.len() {
+            lst += 1;
+            insns.push(get_insn(q[i], q[i + 1]));
+            q.push(lst);
+            i += 2;
+        }
+    }
+    root.circuits.insert(
+        0,
+        Circuit::<C> {
+            num_inputs: n,
+            instructions: insns,
+            constraints: vec![],
+            outputs: vec![lst],
+        },
+    );
+    assert_eq!(root.validate(), Ok(()));
+    root.detect_chains();
+    let (root, _) = root.remove_unreachable();
+    println!("{:?}", root);
+    assert_eq!(root.validate(), Ok(()));
+}
+
+#[test]
+fn test_detect_chains() {
+    test_detect_chains_inner(false, 1);
+    test_detect_chains_inner(false, 2);
+    test_detect_chains_inner(false, 3);
+    test_detect_chains_inner(true, 1);
+    test_detect_chains_inner(true, 2);
+    test_detect_chains_inner(true, 3);
+}