1+/Minimalization

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This page contains attempts on minimizing the number of 1+ instructions, similar to BF instruction minimalization. We also uses the same restrictions that is, there exists a simple translation from X to 1+ and from 1+ to X. A secondary goal is to golf the sum of the number of commands in the submission to which each 1+ command translates for every number of instructions.

If you're to add a submission try your best to explain it.

Minimalization

Combining + and * (Reduced 1 instruction)

Starting with combining + and *. Let's add an & instruction that can do both addition and multiplication:

intermediate   1+
------------------
&              +*

Since a + 0 = a and a * 1 = a it's easy to disable both addition and multiplication:

1+   intermediate
------------------
+    //1\\&
*    111&1<&

Combine Harvester (Reduced 2 instructions)

Now throw " into the mix. Combine it with the & instruction:

CH   intermediate
------------------
@    &"

Disabling " is not as trivial since you need to decrease the length of stack and you can't use @ since it gives you another pair of identical items to get rid of. The only choice is <:

intermediate   CH
------------------
&              @111@1<<^@
"              1111@1<<@

The Lyxal command (Reduced 3 instructions)

The Lyxal command, L, is the 1+ equivalent of the BitChanger command, and it combines \ with ^.

Lyxal   CH
------------------
L       \^
CH   Lyxal
------------------
\    L/L
^    /L    

Properties

These are the properties that a 1+ minimalization language must have.

Property I

There exists an instruction that increases the length of the stack and an instruction that decreases it that does not affect I/O.

If you only have instructions that increases the length of the stack you'll get stuck on translating 1 and " and if you only have decreasers then you cannot do any of +*<.

Notes