Skienna's recursive algorithm for edit distance

Question

I'm having some trouble understanding part of Skienna's algorithm for edit distance presented in his Algorithm Design Manual. I'm posting the recursive version, prior to when he applies dynamic programming to the problem, but my question still stands in that version too I think.

He provides the following code:

#define MATCH       0
#define INSERT      1
#define DELETE      2

int match(char c, char d)
{
    if (c == d) return(0);
    else return(1);
}

int indel(char c)
{
    return(1);
}

int string_compare(char *s, char *t, int i, int j)
{
        int k;                  /* counter */
        int opt[3];             /* cost of the three options */
        int lowest_cost;        /* lowest cost */

        if (i == 0) return(j * indel(' '));
        if (j == 0) return(i * indel(' '));

        opt[MATCH] = string_compare(s,t,i-1,j-1) + match(s[i],t[j]);
        opt[INSERT] = string_compare(s,t,i,j-1) + indel(t[j]);
        opt[DELETE] = string_compare(s,t,i-1,j) + indel(s[i]);

        lowest_cost = opt[MATCH];
        for (k=INSERT; k<=DELETE; k++)
                if (opt[k] < lowest_cost) lowest_cost = opt[k];

        return( lowest_cost );
}

I am having trouble understanding the logic behind how the indices are decremented when arriving at opt[INSERT] and opt[DELETE]. They seem backwards to me.

How can I prove to myself that they are correct?