# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
# ({[i] -> [i+2]} union {[i] -> [i+3]})+;

{[i] -> [Out_1] : Exists ( alpha : 2alpha = i+Out_1 && i <= Out_1-2)} union
 {[i] -> [Out_1] : Exists ( alpha : i < Out_1+2alpha && Out_1+3alpha <= i)}

# 
# R := ({[i] -> [i'] : i'=i+3} union {[i] -> [i'] : i'=i+5} union {[i] -> [i'] : i'=i+7})+;
# 
# R;

{[i] -> [i'] : Exists ( alpha : i+3alpha = i' && i <= i'-3)} union
 {[i] -> [i'] : Exists ( alpha : i < i'+3alpha && 2i'+7alpha <= 2i)} union
 {[i] -> [i'] : Exists ( alpha : i'+3alpha < i && 2i <= 2i'+5alpha)}

# 
# notR := {[i] -> [i'] : i' >= i+3} - R;
# 
# notR;

{[i] -> [i+4] }

# 
# {[i] -> [i'] : i' >= i+3} - notR;

{[i] -> [i+3] } union
 {[i] -> [i'] : i <= i'-5}

# 
# 
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