Parser Help

<S> --> <A><B>
<A> ---> a | b
<B> ---> 1 | 1 <B>

It's suppose to start will a or b and 1 afterward. it doesn't matter how many 1's are after a or b.

/*
<S> --> <A><B>
<A> --->  a | b
<B> --->  1 | 1 <B>

It suppose to be vaild for example: a1, b1, b111111, a111
*/
#include <iostream>
#include<stdlib.h>  // for the exit(1) function
using namespace std;

char text[100];
char ToBeChecked;

char lexical(); //identify the characters
void SProd();
void AProd();
void BProd();
//void CProd();

int main()
{
    cout<<"Enter a string(max. 100 characters"<<endl;
    cin>>text;

    ToBeChecked = lexical(); //identify the character; find the first letter and give it to ToBeChecked
    SProd();

    if(ToBeChecked = '\0')
        cout<<"Valid"<<endl;
        else
        cout<<"Invalid"<<endl;
    cin.get();
    return 0;
}

char lexical()
{
    static int index = -1;   //a memory box named index with a value of -1; is static so it won't change.
                            //is -1 because -1 to 1 is 0; everytime move on to next one
    index++; //update index
    return text[index]; //return the value of index
}
//<S> --> <A> <B>
void SProd()
{
    AProd();
    BProd();
}

//<A> --->  a | b
void AProd()
{


   if(ToBeChecked == 'a'){
   ToBeChecked = lexical();
   }
    else
    {
   if(ToBeChecked == 'b'){
       ToBeChecked = lexical();
       }

    }
}



//<B> --->  1 | 1 <B>
void BProd()
{


   if(ToBeChecked != '1')
    {
      cout<<"Invalid"<<endl;
        exit(1);
    }
       else
       while (ToBeChecked == '1')
            ToBeChecked = lexical();

}