Wierd Machine

The Wierd Machine is a theoretical computer science construct of a 2-cell machine which can implement the cat utility, can(theoretically) implement the Truth-machine and do Flow-down arithmetic (Another theoretical computer model by the author).

Is Wierd a typo?
The 'Wierd Machine' is weird, but not quite. Therefore, it is called the 'Wierd Machine'. So no, it is not a typo.

How it works
There are 6 instructions: I,H, Q, C, L and J Here is a Table of meaning for these functions:

Truth-machine
In theory, it's possible to create a simplification of the machine: ICHQL∞ We get input, compare it with the 2 empty 0 cells, take that as input, Print that forever.

Input=1: 1111111111111111111111111111111111.... Input=0: 0000000000000000000000000000000000.... So, we just need a 'If' statement to make the truth-machine! Details of the Truth-complete Wierd Machine: Statements = I, F, C, H, L, Q F=if

Code of Truth-machine: ICHF0JQI1QL∞ Woohooo! Yahoo! Hurray! A Truth machine in 5 statements! Beat that!

Examples
Wierd Machine-1: Cat program: IQ Input+1: IPQ Wierd machine-2: Doubling IPLIQ