# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
# R := {[i,j] -> [i+3,j]} union {[i,j] -> [i+2,j-1]} union {[i,j] -> [i+1,j+1]};
# 
# R+;

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

# 
# R+ compose R;

{[i,j] -> [Out_1,j'] : Out_1+2j' = i+2j && j' <= j-2} union
 {[i,j] -> [Out_1,j'] : Exists ( alpha : i+j' = j+Out_1+3alpha && 3+i+2j <= Out_1+2j' && 3+i+j' <= j+Out_1)} union
 {[i,j] -> [Out_1,j'] : Exists ( alpha : i+j' = j+Out_1+3alpha && 6+i+2j <= Out_1+2j' && i+j' <= j+Out_1)}

# 
# R - (R+ compose R);

{[i,j] -> [i+2,j-1] } union
 {[i,j] -> [i+1,j+1] }

#