# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
# symbolic n(1);
# 
# R := { [i] -> [j] : 1 <= i = j <= 100 && n(i) <= n(j)};
# 
# S := { [i] -> [j] : 1 <= i <= j <= 100 && n(i) = n(j)};
# 
# 
# R intersection complement S;

{[i] -> [j]  : FALSE }

# 
# inverse R;

{[j] -> [j] : 1 <= j <= 100}

# 
# inverse S;

{[j] -> [j] : 1 <= j <= 100} union
 {[j] -> [i] : n(j) = n(i) && 1 <= i < j <= 100}

# 
# inverse S intersection complement inverse R;

{[j] -> [i] : n(j) = n(i) && 1 <= i < j <= 100}

#