Transmission with dual input and gear ratio multiplication

A transmission, comprising:

• first and second input shafts;
• an output shaft;
• first, second, and third lay shafts;
• a first gear non-rotatably connected to the second lay shaft and a second gear non-rotatably connected to the second input shaft, respectively;
• third and fourth gears meshed with the first and second gears, respectively, so that rotation of the first and second gears causes rotation of the third and fourth gears, respectively;
• a first full synchronizer clutch including:
• a first half synchronizer clutch arranged to non-rotatably connect the third gear to the first lay shaft and to disconnect the third gear from the first lay shaft;
• and,
• a second half synchronizer clutch arranged to non-rotatably connect the fourth gear to the first lay shaft and to disconnect the fourth gear from the first lay shaft;
• and,
• a synchronizer engaged with the first full synchronizer clutch, wherein for a first speed ratio for the transmission, the synchronizer is arranged to non-rotatably connect the third and fourth gears to create a first torque path from the first input shaft to the second lay shaft.