# Omega Calculator [v1.1, Nov 96]:
# #
# # Examples of relations using uninterpreted function symbols
# # from Omega Calculator documentation
# #
# 
# symbolic p(2), n, m;
# 
# R  := { [ir,jr] : 1 <= ir <= n && 1 <= jr <= m };
# 
# W1 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(Set) >= 0 };
# 
# W2 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(Set) <  0 };
# 
# Exposed := R intersection complement ( W1 union W2 );
# 
# Exposed;

{[In_1,In_2]  : FALSE }

# 
# 
# symbolic f(1);
# 
# R1 := { [i] -> [j] : 1 <= i = j <= 100 && f(In) <= f(Out)};
# 
# R2 := { [i] -> [j] : 1 <= i <= j <= 100 && f(In) = f(Out)};
# 
# 
# R1 intersection R2;

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

# 
# R1 union R2;

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

# 
# R1 intersection complement R2;

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

# 
# R1;

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

#