diff --git a/examples/dl2u_error.dl b/examples/dl2u_error.dl
new file mode 100644
index 0000000..610cf23
--- /dev/null
+++ b/examples/dl2u_error.dl
@@ -0,0 +1,5 @@
+source a('A':int, 'B':int).
+source b('B':int, 'C':int).
+view v('A':int, 'B':int, 'C':int).
+-a(A, B) :- a(A, B) , tmp(A, B, C).
+tmp(A, B, C) :- a(A, G) , b(G, C) , B = 60 , G = 30.
diff --git a/examples/dl2u_name.dl b/examples/dl2u_name.dl
new file mode 100644
index 0000000..659ee62
--- /dev/null
+++ b/examples/dl2u_name.dl
@@ -0,0 +1,4 @@
+source a('A':int, 'B':int).
+view v('A':int, 'B':int, 'C':int).
+-a(A, B) :- f(B, A).
+f(C, D) :- a(D, C).
diff --git a/src/ast2sql.ml b/src/ast2sql.ml
index d14ff23..e6b387d 100644
--- a/src/ast2sql.ml
+++ b/src/ast2sql.ml
@@ -2309,9 +2309,6 @@ type grouping_state =
   | NoneState
 
 
-module ArgMap = Map.Make(String)
-
-
 let update_table_env (head : rterm) (body : term list) (table_env : table_environment) : (table_environment, error) result =
   let open ResultMonad in
   let table, args =
@@ -2323,42 +2320,10 @@ let update_table_env (head : rterm) (body : term list) (table_env : table_enviro
   if TableEnv.mem table table_env then
     return table_env
   else
-    args |> List.rev |> foldM (fun (colmns, arg_map) arg ->
+    args |> List.rev |> foldM (fun columns arg ->
       match arg with
-      | NamedVar x -> return (x :: colmns, arg_map |> ArgMap.add x None)
+      | NamedVar x -> return (x :: columns)
       | _          -> err @@ InvalidArgInHead { var = arg; error_detail = InRule (head, body) }
-    ) ([], ArgMap.empty) >>= fun (colmns, arg_map) ->
-    body |> foldM (fun arg_map term ->
-      match term with
-      | Rel (Pred (target, args))
-      | Rel (Deltainsert (target, args))
-      | Rel (Deltadelete (target, args)) ->
-          begin match TableEnv.find_opt target table_env with
-          | None ->
-              err @@ UnknownTable { table = target; error_detail = InRule (head, body) }
-          | Some cols ->
-              List.combine cols args |> foldM (fun arg_map (col, arg) ->
-                match arg with
-                | NamedVar x ->
-                    begin match arg_map |> ArgMap.find_opt x with
-                    | None                             -> err @@ InvalidArgInBody { var = arg; error_detail = InRule (head, body) }
-                    | Some None                        -> return (arg_map |> ArgMap.add x (Some col))
-                    | Some (Some col0) when col = col0 -> return arg_map
-                    | Some (Some _)                    -> err @@ InvalidArgInBody { var = arg; error_detail = InRule (head, body) }
-                    end
-
-                | _          ->
-                    err @@ InvalidArgInBody { var = arg; error_detail = InRule (head, body) }
-              ) arg_map
-          end
-
-      | _ -> return arg_map
-    ) arg_map >>= fun arg_map ->
-    colmns |> List.rev |> foldM (fun columns col ->
-      match arg_map |> ArgMap.find_opt col with
-      | None       -> err @@ HeadVariableDoesNotOccurInBody col
-      | Some None  -> err @@ HeadVariableDoesNotOccurInBody col
-      | Some Some col -> return (col :: columns)
     ) [] >>= fun columns ->
     return @@ TableEnv.add table columns table_env
 
diff --git a/test/ast2sql_operation_based_conversion_test.ml b/test/ast2sql_operation_based_conversion_test.ml
index 5a401b9..0ade920 100644
--- a/test/ast2sql_operation_based_conversion_test.ml
+++ b/test/ast2sql_operation_based_conversion_test.ml
@@ -227,14 +227,14 @@ let main () =
             primary_keys = [];
           };
         expected = String.concat " " [
-          "CREATE TEMPORARY TABLE v AS SELECT a_0.AA AS AA, a_0.BB AS BB, b_1.CC AS CC FROM a AS a_0, b AS b_1 WHERE b_1.BB = a_0.BB;";
-          "CREATE TEMPORARY TABLE temp0 AS SELECT v_0.AA AS AA, v_0.BB AS BB, 3 AS CC FROM v AS v_0 WHERE v_0.CC = 3 AND v_0.AA <> 4;";
-          "CREATE TEMPORARY TABLE temp1 AS SELECT 4 AS AA, temp0.BB AS BB, temp0.CC AS CC FROM temp0 AS temp0;";
-          "CREATE TEMPORARY TABLE uv AS SELECT v_0.AA AS AA, v_0.BB AS BB, v_0.CC AS CC FROM v AS v_0 WHERE NOT EXISTS ( SELECT * FROM temp0 AS t WHERE t.AA = v_0.AA AND t.BB = v_0.BB AND t.CC = v_0.CC ) UNION SELECT temp1.AA AS AA, temp1.BB AS BB, temp1.CC AS CC FROM temp1 AS temp1;";
-          "CREATE TEMPORARY TABLE temp2 AS SELECT uv_0.BB AS BB, uv_0.CC AS CC FROM uv AS uv_0 WHERE NOT EXISTS ( SELECT * FROM b AS t WHERE t.BB = uv_0.BB AND t.CC = uv_0.CC );";
-          "CREATE TEMPORARY TABLE temp3 AS SELECT uv_0.AA AS AA, uv_0.BB AS BB FROM uv AS uv_0 WHERE NOT EXISTS ( SELECT * FROM a AS t WHERE t.AA = uv_0.AA AND t.BB = uv_0.BB );";
-          "CREATE TEMPORARY TABLE temp4 AS SELECT b_0.BB AS BB, b_0.CC AS CC FROM b AS b_0, uv AS uv_1 WHERE uv_1.BB = b_0.BB AND NOT EXISTS ( SELECT * FROM uv AS t WHERE t.BB = b_0.BB AND t.CC = b_0.CC );";
-          "CREATE TEMPORARY TABLE temp5 AS SELECT a_0.AA AS AA, a_0.BB AS BB FROM a AS a_0 WHERE NOT EXISTS ( SELECT * FROM uv AS t WHERE t.AA = a_0.AA AND t.BB = a_0.BB );";
+          "CREATE TEMPORARY TABLE v AS SELECT a_0.AA AS A, a_0.BB AS B, b_1.CC AS C FROM a AS a_0, b AS b_1 WHERE b_1.BB = a_0.BB;";
+          "CREATE TEMPORARY TABLE temp0 AS SELECT v_0.A AS A, v_0.B AS B, 3 AS C FROM v AS v_0 WHERE v_0.C = 3 AND v_0.A <> 4;";
+          "CREATE TEMPORARY TABLE temp1 AS SELECT 4 AS A, temp0.B AS B, temp0.C AS C FROM temp0 AS temp0;";
+          "CREATE TEMPORARY TABLE uv AS SELECT v_0.A AS A, v_0.B AS B, v_0.C AS C FROM v AS v_0 WHERE NOT EXISTS ( SELECT * FROM temp0 AS t WHERE t.A = v_0.A AND t.B = v_0.B AND t.C = v_0.C ) UNION SELECT temp1.A AS A, temp1.B AS B, temp1.C AS C FROM temp1 AS temp1;";
+          "CREATE TEMPORARY TABLE temp2 AS SELECT uv_0.B AS BB, uv_0.C AS CC FROM uv AS uv_0 WHERE NOT EXISTS ( SELECT * FROM b AS t WHERE t.BB = uv_0.B AND t.CC = uv_0.C );";
+          "CREATE TEMPORARY TABLE temp3 AS SELECT uv_0.A AS AA, uv_0.B AS BB FROM uv AS uv_0 WHERE NOT EXISTS ( SELECT * FROM a AS t WHERE t.AA = uv_0.A AND t.BB = uv_0.B );";
+          "CREATE TEMPORARY TABLE temp4 AS SELECT b_0.BB AS BB, b_0.CC AS CC FROM b AS b_0, uv AS uv_1 WHERE uv_1.B = b_0.BB AND NOT EXISTS ( SELECT * FROM uv AS t WHERE t.B = b_0.BB AND t.C = b_0.CC );";
+          "CREATE TEMPORARY TABLE temp5 AS SELECT a_0.AA AS AA, a_0.BB AS BB FROM a AS a_0 WHERE NOT EXISTS ( SELECT * FROM uv AS t WHERE t.A = a_0.AA AND t.B = a_0.BB );";
           "INSERT INTO b SELECT * FROM temp2;";
           "INSERT INTO a SELECT * FROM temp3;";
           "DELETE FROM b USING temp4 WHERE b.BB = temp4.BB AND b.CC = temp4.CC;";