// Ackermann Function
//
// fun ack(0,n) = n+1
//   | ack(m,0) = ack(m-1,1)        
//   | ack(m,n) = ack(m-1,ack(m,n-1));

// The below rule is wrong because there is no gurantee that
// the 'cnt' is an integer agent when ack(r)~(m-1,cnt) is evaluated.
//
// ack(r) >< (int m, int n)
// | m==0 => r~(n+1)
// | n==0 => ack(r) ~ (m-1,1)
// | _ => ack(cnt)~(m,n-1), ack(r)~(m-1,cnt);


ack(ret, n) >< (int m)
| m==0 => inc(ret)~n
| _ => ackn(ret, m)~n;

ackn(ret, int m) >< (int n)
| n==0 => ack(ret,1) ~ (m-1)
| _ => ack(cnt,n-1)~m, ack(ret,cnt)~(m-1);

inc(ret)><(int n) => ret~(n+1);


ackMain(ret)><(int m, int n) => ack(ret,n)~m;

ackMain(ret)~(3,5);
ret;
free ret;