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For it to remain Touring complete we need instructions:
1) +, replaces -, *, so also % and mod when used cleverly
2) and, or, not, elementary logical operations
3) if else operations, needed for the program to work properly
4) the < operation, it replaces the rest
5) functions, using variables, they will replace loops and allow to execute each program
After such a reduction we have less states, but we are able to operate so cleverly on the possessed that the reduction does not break our touring complete.