Take:
int len(int f, int l) {
 return l < f ? 0 : l - f + 1;
}

int lenzero(int f, int l) {
 return len(f, l) == 0;
}

int g(); int h();
int lenzero1(int f, int l) {
 if ( len(f, l) == 0)
   return g();
  return h();
}

we should be able to optimize lenzero at -O1 but don't.  lenzero1 is optimized at -O1 because dom is able to jump thread.
The difference in IR is:
  # iftmp.0_9 = PHI <0(2), iftmp.0_8(3)>
  _2 = iftmp.0_9 == 0;

vs:
  # iftmp.0_13 = PHI <0(2), iftmp.0_12(3)>
  if (iftmp.0_13 == 0)

at -O2 PRE is enabled which does the optimization.
This is similar to spaceship_replacement in tree-ssa-phiopt but a more general statement of the problem.