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# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
# symbolic n;
#
# I := {[i,j,k] : 1 <= i,j,k <= n};
#
# R1 := {[i,j,n] -> [i,j+1,1] : 1 <= i,j,j+1 <= n}
# union {[i,j,k] -> [i,j,k'] : 1 <= i,j,k,k' <= n && k' = k+1};
#
# R1;
{[i,j,n] -> [i,j+1,1] : 1 <= i <= n && 1 <= j < n} union
{[i,j,k] -> [i,j,k+1] : 1 <= i <= n && 1 <= j <= n && 1 <= k < n}
#
# R1+;
{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
{[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
#
# R1+ within I;
{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
{[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
#
# R2 := {[i,n,n] -> [i+1,1,1] : 1 <= i,i+1 <= n}
# union R1;
#
# R2;
{[i,n,n] -> [i+1,1,1] : 1 <= i < n} union
{[i,j,k] -> [i,j,k+1] : 1 <= i <= n && 1 <= j <= n && 1 <= k < n} union
{[i,j,n] -> [i,j+1,1] : 1 <= i <= n && 1 <= j < n}
#
# R2+;
{[i,j,k] -> [i',j',k'] : 1 <= i < i' <= n && 1 <= j <= n && 1 <= k <= n && 1 <= j' <= n && 1 <= k' <= n} union
{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
{[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
#
# R2+ within I;
{[i,j,k] -> [i',j',k'] : 1 <= i < i' <= n && 1 <= j <= n && 1 <= k <= n && 1 <= j' <= n && 1 <= k' <= n} union
{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
{[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
#
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