# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
# R := { [i] -> [i'] : 1 <= i,i' <= 10 && i' = i+1 };
# 
# R;

{[i] -> [i+1] : 1 <= i <= 9}

# 
# inverse R;

{[i] -> [i-1] : 2 <= i <= 10}

# 
# domain R;

{[i]: 1 <= i <= 9}

# 
# range R;

{[i]: 2 <= i <= 10}

# 
# R compose R;

{[i] -> [i+2] : 1 <= i <= 8}

# 
# R+;

{[i] -> [i'] : 1 <= i < i' <= 10}

#              # closure of R = R union (R compose R) union (R compose R ...
# complement R;

{[i] -> [i'] : i <= 0} union
 {[i] -> [i'] : 10 <= i} union
 {[i] -> [i'] : 1 <= i <= 9, i'-2} union
 {[i] -> [i'] : 1, i' <= i <= 9}

# 
# S := {[i] : 5 <= i <= 25};
# 
# S;

{[i]: 5 <= i <= 25}

# 
# R(S);

{[i]: 6 <= i <= 10}

#            # apply R to S
# R \ S;

{[i] -> [i+1] : 5 <= i <= 9}

#           # restrict domain of R to S
# R / S;

{[i] -> [i+1] : 4 <= i <= 9}

#           # restrict range of R to S
# (R\S) union (R/S);

{[i] -> [i+1] : 4 <= i <= 9}

# 
# (R\S) intersection (R/S);

{[i] -> [i+1] : 5 <= i <= 9}

# 
# (R/S) - (R\S);

{[4] -> [5] }

# 
# S*S;

{[i] -> [i'] : 5 <= i <= 25 && 5 <= i' <= 25}

#             # cross product 
# D := S - {[9:16:2]} - {[17:19]};
# 
# D;

{[i]: 5 <= i <= 8} union
 {[i]: Exists ( alpha : 2alpha = i && 10 <= i <= 16)} union
 {[i]: 20 <= i <= 25}

# 
# T :=  { [i] : 1 <= i <= 11 & exists (a : i = 2a) };
# 
# T;

{[i]: Exists ( alpha : 2alpha = i && 2 <= i <= 10)}

# 
# Hull T;

{[i]: 2 <= i <= 10}

# 
# Hull D;

{[i]: 5 <= i <= 25}

# 
# codegen D;
for(t1 = 5; t1 <= 8; t1++) {
  s1(t1);
}
for(t1 = 10; t1 <= 16; t1 += 2) {
  s1(t1);
}
for(t1 = 20; t1 <= 25; t1++) {
  s1(t1);
}

# 
# codegen {[i,j] : 1 <= i+j,j <= 10};
for(t1 = -9; t1 <= 9; t1++) {
  for(t2 = max(-t1+1,1); t2 <= min(-t1+10,10); t2++) {
    s1(t1,t2);
  }
}

#