CounterScript

CounterScript is a Turing-complete minimal counter-based esolang. It was created in 2026 by Azerty specifically for program enumeration and analysis. CS features a very small instruction set operating over an unbounded set of nonnegative integer variables (counters). What make this esolang interesting is that it takes longer programs to compute chaotic/spaghetti functions, compared to Turing machines.

BBCS(n) is the Busy Beaver function for CounterScript programs.

Definition

A CounterScript program consists of a finite sequence of instructions drawn from three primitives:

• Increment a counter
• Conditional decrement
• While loop

All counters are initialized to 0 and can grow without bound.

The model is closely related to register machines, FRACTRAN and brainfuck. It can simulate Boolfuck, and is therefore Turing-complete.

Instructions

Instructions are executed one by one from left to right.

Name	Command	Definition
Increment	A++;	Increment counter A by 1
Decrement	A--;	Decrement counter A by 1 if A > 0
While loop	while A {...}	Executes the loop body while A > 0

Macros

In order to improve readability we define the following macros.

	Macro	Definition	Size	Function
Constant Addition	A+=n;	increment A by n	n	A++; repeated n times
Transfer	A>>B*n;	increment B by A*n then set A to 0	n+2	while A {A--; (B++; repeated n times)}

Champions

The Busy Beaver function for CounterScript, denoted BBCS(n), returns the largest score a CounterScript program of length n can have when halting.

The score of a program is the maximum value of its counters.

The length of a CounterScript program is defined as the total number of instructions.

By example, A++; B++; while A {A--; C++; C++;} has length 6 and its score is 2.

n	BBCS(n)	Champion	Counters upon halting
1	1	A++;	1
2	2	A+=2;	2
3	3	A+=3;	3
4	4	A+=4;	4
5	5	A+=5;	5
6	6	A+=6;	6
7	7	A+=7;	7
8	9	A+=3; A>>B*3;	0 9
9	12	A+=4; A>>B*3;	0 12
10	16	A+=4; A>>B*4;	0 16
11	20	A+=5; A>>B*4;	0 20
12	≥ 25	A+=5; A>>B*5;	0 25
13	≥ 42	A++; while A {A++; while B {A--; B--; C+=2;} C>>B*2; C++;}	0 42 1
14	≥ 129	A++; while A {A++; while B {A--; B--; C+=2;} C>>B*3; C++;}	0 129 1
15	≥ 340	A+=4; while A {A--; B++; B>>C*2; C>>B*2;}	0 340 0
16	≥ 1,554	A+=4; while A {A--; B++; B>>C*3; C>>B*2;}	0 1554 0
17	≥ 9,330	A+=5; while A {A--; B++; B>>C*3; C>>B*2;}	0 9330 0
18	≥ 66,429	A+=5; while A {A--; B++; B>>C*3; C>>B*3;}	0 66429 0
19	≥ (3^122 - 3)/2	A++; while A {A++; while B {A--; B--; C++;} while C {B++; C--; B>>D*3; D>>B;} C++;}	0 (3^122-3)/2 1
20	≥ 2^65536 - 2	A+=4; while A {A--; B++; while B {B--; C++; C>>D*2; D>>C;} C>>B;}	0 2^65536-2 0 0
21	≥ 2^2^65536 - 2	A+=5; while A {A--; B++; while B {B--; C++; C>>D*2; D>>C;} C>>B;}	0 2^2^65536-2 0 0
22	≥ 2^^7 - 2	A+=6; while A {A--; B++; while B {B--; C++; C>>D*2; D>>C;} C>>B;}	0 2^^7-2 0 0
23	≥ 2^^8 - 2	A+=7; while A {A--; B++; while B {B--; C++; C>>D*2; D>>C;} C>>B;}	0 2^^8-2 0 0
24	≥ 2^^65536 - 2	A++; while A {A++; while B {A--; B--; C++;} while C {B++; C--; while B {B--; D++; D>>E*2; E>>D;} D>>B;} C++;}
25	> 2^^2^^6	A++; while A {A++; while B {A--; B--; C+=2;} while C {B++; C--; while B {B--; D++; D>>E*2; E>>D;} D>>B;} C++;}
26	≥ 2^^2^^65536 - 2	A+=4; while A {A--; B++; while B {B--; C++; while C {C--; D++; D>>E*2; E>>D;} D>>C;} C>>B;}	0 2^^2^^65536-2 0 0 0
64	> Graham's number	too large to show, see Discord
85	> q(5) (if extant)	too large to show, see Discord

Cryptids

No cryptids have been found through exhaustive search of a domain. The smallest known cryptid, a Hydra variant, is of length 23.

A++; B++; while B {
  while A {
    A--; C++; E++;
    while D {D--; E--;}
    while E {C++; D++; E--;}
  }
  C>>A; D>>B*3; B--;
}

// start -> (1, 1)
// (2a, b+1) -> (3a, b)
// (2a+1, b) -> (3a+2, b+2)
// (a, 0) -> halt