SSA variables elimination

Question

There is a program which is in SSA form. Is there an algorithm to simplify the program?

For example,

for(int vlc1 = 0; vlc1 < N; vlc1++) {
  int v1 = a[vlc1];
  int v2 = 100;
  int v3 = v1 + v2;
  a[vlc1+1] = v3;
}

This example can be simplified to:

for(int vlc1 = 0; vlc1 < N; vlc1++) {
  a[vlc1+1] = a[vlc1] + 100;
}

And there is an another example,

int v0 = a[0];
for(int vlc1 = 0; vlc1 < N; vlc1++) {
  int v1 = a[vlc1];
  int v2 = 100;
  int v3 = v1 + v2;
  a[vlc1+1] = v3;
}
int v4 = a[0] / v0;

This example can be simplified to:

int v0 = a[0];
for(int vlc1 = 0; vlc1 < N; vlc1++) {
  a[vlc1] = a[vlc1+1] + 100;
}
int v4 = a[0] / v0;