diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index 11023bb1cd..4f232409a2 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -1553,36 +1553,43 @@ private function specifyTypesFromAsserts(TypeSpecifierContext $context, Expr\Cal
 
 		foreach ($asserts as $assert) {
 			foreach ($argsMap[substr($assert->getParameter()->getParameterName(), 1)] ?? [] as $parameterExpr) {
-				$assertedType = TypeTraverser::map($assert->getType(), static function (Type $type, callable $traverse) use ($argsMap, $scope): Type {
-					if ($type instanceof ConditionalTypeForParameter) {
-						$parameterName = substr($type->getParameterName(), 1);
-						if (array_key_exists($parameterName, $argsMap)) {
-							$argType = TypeCombinator::union(...array_map(static fn (Expr $expr) => $scope->getType($expr), $argsMap[$parameterName]));
-							$type = $type->toConditional($argType);
+				$assertedType = $assert->getType();
+
+				if ($assertedType->hasTemplateOrLateResolvableType()) {
+					$assertedType = TypeTraverser::map($assertedType, static function (Type $type, callable $traverse) use ($argsMap, $scope): Type {
+						if ($type instanceof ConditionalTypeForParameter) {
+							$parameterName = substr($type->getParameterName(), 1);
+							if (array_key_exists($parameterName, $argsMap)) {
+								$argType = TypeCombinator::union(...array_map(static fn (Expr $expr) => $scope->getType($expr), $argsMap[$parameterName]));
+								$type = $type->toConditional($argType);
+							}
 						}
-					}
 
-					return $traverse($type);
-				});
+						return $traverse($type);
+					});
+				}
 
 				$assertExpr = $assert->getParameter()->getExpr($parameterExpr);
 
-				$templateTypeMap = $parametersAcceptor->getResolvedTemplateTypeMap();
 				$containsUnresolvedTemplate = false;
-				TypeTraverser::map(
-					$assert->getOriginalType(),
-					static function (Type $type, callable $traverse) use ($templateTypeMap, &$containsUnresolvedTemplate) {
-						if ($type instanceof TemplateType && $type->getScope()->getClassName() !== null) {
-							$resolvedType = $templateTypeMap->getType($type->getName());
-							if ($resolvedType === null || $type->getBound()->equals($resolvedType)) {
-								$containsUnresolvedTemplate = true;
-								return $type;
+				if ($assert->getOriginalType()->hasTemplateOrLateResolvableType()) {
+					$templateTypeMap = $parametersAcceptor->getResolvedTemplateTypeMap();
+
+					TypeTraverser::map(
+						$assert->getOriginalType(),
+						static function (Type $type, callable $traverse) use ($templateTypeMap, &$containsUnresolvedTemplate) {
+							if ($type instanceof TemplateType && $type->getScope()->getClassName() !== null) {
+								$resolvedType = $templateTypeMap->getType($type->getName());
+								if ($resolvedType === null || $type->getBound()->equals($resolvedType)) {
+									$containsUnresolvedTemplate = true;
+									return $type;
+								}
 							}
-						}
 
-						return $traverse($type);
-					},
-				);
+							return $traverse($type);
+						},
+					);
+				}
 
 				$newTypes = $this->create(
 					$assertExpr,
diff --git a/src/Rules/Classes/LocalTypeAliasesCheck.php b/src/Rules/Classes/LocalTypeAliasesCheck.php
index a849ecac8c..d5851b28b5 100644
--- a/src/Rules/Classes/LocalTypeAliasesCheck.php
+++ b/src/Rules/Classes/LocalTypeAliasesCheck.php
@@ -335,8 +335,8 @@ private function isAliasNameValid(string $aliasName, ?NameScope $nameScope): boo
 		}
 
 		$aliasNameResolvedType = $this->typeNodeResolver->resolve(new IdentifierTypeNode($aliasName), $nameScope->bypassTypeAliases());
-		return ($aliasNameResolvedType->isObject()->yes() && !in_array($aliasName, ['self', 'parent'], true))
-			|| $aliasNameResolvedType instanceof TemplateType; // aliases take precedence over type parameters, this is reported by other rules using TemplateTypeCheck
+		return $aliasNameResolvedType instanceof TemplateType || // aliases take precedence over type parameters, this is reported by other rules using TemplateTypeCheck
+			($aliasNameResolvedType->isObject()->yes() && !in_array($aliasName, ['self', 'parent'], true));
 	}
 
 	/**
diff --git a/src/Rules/FunctionDefinitionCheck.php b/src/Rules/FunctionDefinitionCheck.php
index c888ed886f..8923179a82 100644
--- a/src/Rules/FunctionDefinitionCheck.php
+++ b/src/Rules/FunctionDefinitionCheck.php
@@ -591,6 +591,10 @@ private function checkParametersAcceptor(
 		$templateTypes = $templateTypeMap->getTypes();
 		if (count($templateTypes) > 0) {
 			foreach ($parametersAcceptor->getParameters() as $parameter) {
+				if (!$parameter->getType()->hasTemplateOrLateResolvableType()) {
+					continue;
+				}
+
 				TypeTraverser::map($parameter->getType(), static function (Type $type, callable $traverse) use (&$templateTypes): Type {
 					if ($type instanceof TemplateType) {
 						unset($templateTypes[$type->getName()]);
diff --git a/src/Rules/PhpDoc/ConditionalReturnTypeRuleHelper.php b/src/Rules/PhpDoc/ConditionalReturnTypeRuleHelper.php
index af7cfda155..0224209b0c 100644
--- a/src/Rules/PhpDoc/ConditionalReturnTypeRuleHelper.php
+++ b/src/Rules/PhpDoc/ConditionalReturnTypeRuleHelper.php
@@ -77,14 +77,16 @@ public function check(ExtendedParametersAcceptor $acceptor): array
 					continue;
 				}
 				$templateTypes = [];
-				TypeTraverser::map($subjectType, static function (Type $type, callable $traverse) use (&$templateTypes): Type {
-					if ($type instanceof TemplateType) {
-						$templateTypes[] = $type;
-						return $type;
-					}
-
-					return $traverse($type);
-				});
+				if ($subjectType->hasTemplateOrLateResolvableType()) {
+					TypeTraverser::map($subjectType, static function (Type $type, callable $traverse) use (&$templateTypes): Type {
+						if ($type instanceof TemplateType) {
+							$templateTypes[] = $type;
+							return $type;
+						}
+
+						return $traverse($type);
+					});
+				}
 
 				if (count($templateTypes) === 0) {
 					$errors[] = RuleErrorBuilder::message(sprintf('Conditional return type uses subject type %s which is not part of PHPDoc @template tags.', $subjectType->describe(VerbosityLevel::typeOnly())))