## 2 Materials and Methods  
The sample size of the experiment was calculated using the GPower (3.1.9.7, Universitat Kiel, Dussendorf, Germany) with the power of 0.9, \(\alpha=0.05\), and the effect size of 1.6. The result of the sample size was 10 files for each experimental group. A total of 30 NiTi files, 20 instruments of ProTaper Universal F2 (Dentsply Sirona, Maillefer, Ballaigues, Switzerland), 10 instruments of ProTaper Next X2 (Dentsply Sirona, Maillefer, Ballaigues, Switzerland) with the length of 25 mm for the instruments were included in the present study. All instruments were unused and new as delivered. Instruments were evaluated using a dental operating microscope at a magnification of 10 (CJ Optik GmbH & Co. KG, A\(\&\)lar-Werdorf, Germany) concerning any deformations or imperfections on the surface, including the edge and the flute, along the length of the instruments. A framework, including a gear for holding the endodontic handpiece (X-Smart Plus, Dentsply Sirona, Maillefer, Ballaigues, Switzerland), and a glass box of sewing machine oil (Shell Morlina 10, Shell Corp., Ho Chi Minh City, Viet Nam) containing the artificial canal was constructed to evaluate the cyclic fatigue resistance of the instruments. For the static cycles experiment, the files of group 1 (10 PTU F2) rotated at the full length of the artificial canal until they broke. A step motor drove a screw that moved the gear containing the endodontic handpiece. This step motor was controlled by a programmable module that might change or control the motion of the gear as desired. The step motor had a specification of 1.8\({}^{\circ}\)/step, needing 200 steps to complete a full rotation of 360\({}^{\circ}\). The pitch of the lead screw of the framework was 5 mm. The digital controller was set to move the stainless steel block containing the double-curved canal following the desired modes. For the dynamic cycles, the files of the two groups, group 2 (10 PTU F2) and group 3 (10 PTN X2), were used for the experiment. The motion mode was set as in-and-out with a fixed distance until the instrument broke. A body temperature environment was created using sewing machine oil to sustain the temperature and lubricate the instrument in a glass box. The temperature (37 \({}^{\circ}\)C \(\pm\) 0.5 \({}^{\circ}\)C) of the glass box was maintained using a thermostat and heating device. The stainless steel block containing the artificial canal was produced using a special technique for the double-curved canal with technique parameters, as described elsewhere [22]. The entire length of the artificial canal was 18 mm with a diameter of 1.5 mm. There were two curved segments along the length of the stainless steel canal. The first curved segment's center was at 2 mm from the apex with the angle and the radius of 70\({}^{\circ}\) and 2 mm, respectively. The second curved segment's center was at 8 mm from the apex with the angle and the radius of 60\({}^{\circ}\) and 5 mm, respectively. In the sewing machine oil, the artificial canal was immobile. The handpiece of the endodontic motor was fixed on the gear designed especially for the X-Smart Plus (Dentsply Sirona, Maillefer, Ballaigues, Switzerland). The gear can be displaced in or out at any distance for each kind of motion, programmed by the operator for control through a liquid crystal display (LCD) interface with function keys. A stopwatch was placed next to the glass box, and a digital camera Canon 70D (Canon, Tokyo, Japan), was used to capture the entire process from the beginning of movement until the instrument's fracture. The time was recorded for the rotation of the intact file and multiplied by the round per minute (RPM) of each kind of instrument, as instructed by the manufacturer, for the number of cycles. The phase at which the file fracture occurred was recorded whether it happened during the in-or-out phase or at the full length of the canal.