# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
# #
# # Extract from omega4
# #  removed "eqnarray" commands, associated &'s, and overbrace commands
# #  added declaration of n
# #  added semicolon
# #
# # It would be nice not to have to do the following:
# #  removed \ in front of variable names
# # 
# 
# $$
# symbolic n;
# 
# R := \{\ [ii] \rightarrow [ki] \mid
# 1 \leq ii \leq 2n
# 	\ \land \  1 \leq ki \leq 2n
# \land ii = ki 
# \land ii = ki\\
# \t \land 
# 	\ \neg (\ \exists [ji, jj] \st
# (1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
# \land (ii \leq ji \land ji \leq ki) \land (2jj = ki)\ )\\ 
# \t 
# \land \ 
# \neg (\ \exists [ji, jj] \st
# (1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
# \land (ii \leq ji \land ji \leq ki) \land (2jj\!+\!1 = ki)\ )
# \   \}
# ;
# 
# 
# R;

{[ii] -> [ii] : n = 1 && 1 <= ii <= 2} union
 {[2n] -> [2n] : 2 <= n} union
 {[1] -> [1] : 2 <= n}

# 
# $$
# # S := \{\ [\ii] \rightarrow [\ki] \mid
# # 1 \leq \ii \leq 2\n
# # 	\ \land \  1 \leq \ki \leq 2\n
# # \land \ii = \ki 
# # \land \ii = \ki\\
# # \t \land 
# # 	\ \neg (\ \exists [\ji, \jj] \st
# # (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
# # \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj = \ki)\ )\\ 
# # \t 
# # \land \ 
# # \neg (\ \exists [\ji, \jj] \st
# # (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
# # \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj\!+\!1 = \ki)\ )
# # \   \}
# # ;
# # 
# # S;