Hidden in those 301 years

Hidden in those 301 years(HT3Y), is an esoteric programming language created by User:Yayimhere, with the goal of being Turing complete, while also not having any characters repeating in a program.

Syntax

HT3Y uses tokens. A token is a bracket surrounded string. A group of tokens with the same length n, is called a group over length n. Every program made up of these tokens follow these rules:

• No token may repeat.
• No token in a group over length n may share characters with another token in the same group. The subgroups were all tokens follow this is called as strict group over length n.
• No token may have characters repeat inside of themselves.

Memory

Every token acts as a variable, having a unique integer value, negative or not. The first variable is -1 at the start, the second is 1, with every over being 0. There is also a pointer, pointing to one variable at all times. The pointer starts at the the second variable in the program.

Semantics

Say we are currently pointing to variable v1, and the one left to it is v2. Then, the following process is done:

k=v2
v2+=v1
v1=(3+k)*(|k-1|)

In other words, k is set to v2, then v2 is incremented by v1, and then last, v1 is set to 3+k times the absolute value of k-1. And then the pointer moves left by one. Note that when the pointer reaches one cell away from the degree of the program, the program is reversed, still keeping the pointer on the same variable. An example could be:

(e)(a)(c)(i)

which computes as:

e=-1, a=1 -> e=0, a=4
a=4, c=0 -> a=4, c=21
c=21, i=0 -> c=21, i=480
i=480, c=21 -> i=501, 231357

as you can see, values grow exponentially(I think) fast.