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# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
# symbolic N,M,k;
#
# { [i,j] -> [] : 0 <= i <= M and 0 <= j <= N and 2i+j = k
# and NOT( exists [i2,j2] :
# 0 <= i2 <= M and 0 <= j2 <= N
# and 2i2+j2 = k
# and i < i2 ) };
{[i,k-2i] -> : 2i <= k <= 2i+1 && 0 <= i <= M && k <= N+2i} union
{[M,k-2M] -> : 2+2M <= k && k <= N+2M && 0 <= M}
#
# { [i,j] -> [] : 0 <= i <= M and 0 <= j <= N and 2i+j = k
# and NOT( i < M && 2i-2 <= k &&
# N-k <= 2M
# && ( N-k < k or N <= 2k && (exists a : k = 2 a)
# ))};
{[i,k-2i] -> : 0 <= i <= M && 2M+k < N && 2i <= k} union
{[M,k-2M] -> : N <= 2M+k && k <= N+2M && 2M <= k} union
{[i,k-2i] -> : 2k < N && N <= 2M+k && 0 <= i && 2i <= k} union
{[i,k-2i] -> : Exists ( alpha : N = 2k && 2i = 1+k+2alpha && 2i+1 <= k <= 2M-1 && 0 <= i)}
#
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