diff --git a/lib/typeprof/core/graph/box.rb b/lib/typeprof/core/graph/box.rb
index a0be290c1..dc359c09c 100644
--- a/lib/typeprof/core/graph/box.rb
+++ b/lib/typeprof/core/graph/box.rb
@@ -213,6 +213,7 @@ def resolve_overload(changes, genv, method_type, node, param_map, a_args, ret, f
         end
         return false
       end
+
       if rbs_blk && a_args.block
         # rbs_blk_func.optional_keywords, ...
         blk_a_args = rbs_blk.req_positionals.map do |blk_a_arg|
@@ -251,6 +252,20 @@ def resolve_overloads(changes, genv, node, param_map, a_args, ret, &blk)
         return
       end
 
+      # If any positional argument has no type information, we cannot
+      # determine which overload to select. Return silently (untyped)
+      # rather than attempting to match. This prevents oscillation in
+      # cyclic cases like @x = Foo.transform(@x), and avoids false
+      # "failed to resolve overloads" diagnostics for untyped arguments.
+      # We still set up dependency edges so the box re-runs when the
+      # empty arguments later receive types.
+      if a_args.positionals.any? {|vtx| vtx.types.empty? }
+        a_args.positionals.each do |vtx|
+          changes.add_edge(genv, vtx, changes.target)
+        end
+        return
+      end
+
       match_any_overload = false
       @method_types.each do |method_type|
         if resolve_overload(changes, genv, method_type, node, param_map, a_args, ret, false, &blk)
diff --git a/scenario/rbs/untyped-for-overload-record.rb b/scenario/rbs/untyped-for-overload-record.rb
index 653ca874a..cfc83a88d 100644
--- a/scenario/rbs/untyped-for-overload-record.rb
+++ b/scenario/rbs/untyped-for-overload-record.rb
@@ -13,5 +13,5 @@ def check(unknown)
 
 ## assert
 class Object
-  def check: (untyped) -> (:record | :str)
+  def check: (untyped) -> untyped
 end
diff --git a/scenario/rbs/untyped-for-overload-singleton.rb b/scenario/rbs/untyped-for-overload-singleton.rb
index 9933790ca..df4c5ae72 100644
--- a/scenario/rbs/untyped-for-overload-singleton.rb
+++ b/scenario/rbs/untyped-for-overload-singleton.rb
@@ -13,5 +13,5 @@ def check(unknown)
 
 ## assert
 class Object
-  def check: (untyped) -> (:int | :str)
+  def check: (untyped) -> untyped
 end
diff --git a/scenario/rbs/untyped-for-overload-tuple.rb b/scenario/rbs/untyped-for-overload-tuple.rb
index 62b4a2ee4..0411c6119 100644
--- a/scenario/rbs/untyped-for-overload-tuple.rb
+++ b/scenario/rbs/untyped-for-overload-tuple.rb
@@ -13,5 +13,5 @@ def check(unknown)
 
 ## assert
 class Object
-  def check: (untyped) -> (:str | :tuple)
+  def check: (untyped) -> untyped
 end
diff --git a/scenario/rbs/untyped-for-overload.rb b/scenario/rbs/untyped-for-overload.rb
index 529e6cf3e..620f85d29 100644
--- a/scenario/rbs/untyped-for-overload.rb
+++ b/scenario/rbs/untyped-for-overload.rb
@@ -11,5 +11,5 @@ def check
 
 ## assert
 class Object
-  def check: -> (:A | :B)
+  def check: -> untyped
 end
diff --git a/scenario/regressions/avoid-infinite-loop-overload-chain.rb b/scenario/regressions/avoid-infinite-loop-overload-chain.rb
new file mode 100644
index 000000000..4cf255c35
--- /dev/null
+++ b/scenario/regressions/avoid-infinite-loop-overload-chain.rb
@@ -0,0 +1,18 @@
+## update: test.rbs
+class Foo
+  def self.transform: (Integer) -> String
+                    | (String) -> Float
+                    | (Float) -> Symbol
+end
+
+## update: test.rb
+def check
+  @x = Foo.transform(@x)
+end
+
+## diagnostics: test.rb
+
+## assert
+class Object
+  def check: -> untyped
+end
diff --git a/scenario/regressions/avoid-infinite-loop-overload-disjoint.rb b/scenario/regressions/avoid-infinite-loop-overload-disjoint.rb
new file mode 100644
index 000000000..0832f2462
--- /dev/null
+++ b/scenario/regressions/avoid-infinite-loop-overload-disjoint.rb
@@ -0,0 +1,17 @@
+## update: test.rbs
+class Foo
+  def self.transform: (Integer) -> Float
+                    | (String) -> Symbol
+end
+
+## update: test.rb
+def check
+  @x = Foo.transform(@x)
+end
+
+## diagnostics: test.rb
+
+## assert
+class Object
+  def check: -> untyped
+end
diff --git a/scenario/regressions/avoid-infinite-loop-overload-partial.rb b/scenario/regressions/avoid-infinite-loop-overload-partial.rb
new file mode 100644
index 000000000..c5153e1e4
--- /dev/null
+++ b/scenario/regressions/avoid-infinite-loop-overload-partial.rb
@@ -0,0 +1,17 @@
+## update: test.rbs
+class Foo
+  def self.transform: (Integer) -> String
+                    | (String) -> Float
+end
+
+## update: test.rb
+def check
+  @x = Foo.transform(@x)
+end
+
+## diagnostics: test.rb
+
+## assert
+class Object
+  def check: -> untyped
+end