Not sure what the purpose of the relay box is though.
A traditional relay is an electromagnetic device that allows you to control a device, typically one that requires a lot of power one such as lights, a motor, or a heater, with a much device that uses a much smaller amount of power. Your low power circuit controls an electromagnet. The electromagnet operates a switch that controls the current to the high power device.
A solid state relay uses an LED in it's low power circuit. This LED controls a transistor (or other similar device) which in turn controls the current to the high power device.
We need to know what kind of signal the 'rayexelec' expects to find at it's input (the low power side) and then use the Arduino to generate this signal.
Have you ever heard of a device called a Powerswitch Tail? This may be just what you need.
Don