diff --git a/python/mscclpp/language/ir.py b/python/mscclpp/language/ir.py
index 16a5b67f..3a1408ac 100644
--- a/python/mscclpp/language/ir.py
+++ b/python/mscclpp/language/ir.py
@@ -331,7 +331,9 @@ class _NopConverter(_OpConverter):
     def to_json(self, op: Op, tb_channel_dict: dict) -> _JsonInstruction:
         return _JsonInstruction(
             name=op.inst.value,
-            deps=list(map(lambda dep: {"tb": dep.tb, "step": dep.step}, op.depends)),
+            deps=sorted(
+                list(map(lambda dep: {"tb": dep.tb, "step": dep.step}, op.depends)), key=lambda x: (x["tb"], x["step"])
+            ),
         )
 
 
diff --git a/python/mscclpp/language/utils.py b/python/mscclpp/language/utils.py
index c97af881..02432b70 100644
--- a/python/mscclpp/language/utils.py
+++ b/python/mscclpp/language/utils.py
@@ -37,6 +37,7 @@ def merge_op(op: Op, other_op: Op):
 def circular_dep_after_merge(op: Op, other_op: Op):
     root = set([op, other_op])
     frontier = set(op.next)
+    visited = set()
     if other_op in frontier:
         frontier.remove(other_op)
     frontier = list(frontier.union(other_op.next))
@@ -46,7 +47,9 @@ def circular_dep_after_merge(op: Op, other_op: Op):
             # The root node will be visited again if there is a circular dependency
             if n in root:
                 return True
-            frontier.append(n)
+            if n not in visited:
+                frontier.append(n)
+                visited.add(n)
         frontier = frontier[1:]