Computing Ackerman number for inputs in JavaScript

Ackermann Function

The Ackermann Function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.

Problem

We are required to write a JavaScript function that takes in two numbers, m and n as the first and the second argument. Our function should return the Ackermann number A(m,n) defined by

A(m,n) = n+1 if m=0
A(m,n) = A(m-1,1) if m>0 , n=0
A(m,n) = A(m-1,A(m,n-1)) if m,n > 0

Example

const m = 12;
const n = 11;
const ackermann = (m, n) => {
   if (m === 0) {
      return n+1
   }
   if (n === 0) {
      return ackermann((m - 1), 1);
   }
   if (m !== 0 && n !== 0) {
      return ackermann((m-1), ackermann(m, (n-1)))
   }
}
console.log(ackermann(m, n));