bash-3.00$ cat e14.in 
# Philippe's simple example
#--------------------------
# 1 <= i <= N
# 1 <= j <= N
# 1 <= k <= N
# i+j+k-2 = M
#--------------------------
7 7
#  i  j  k  N  M  1
1  1  0  0  0  0 -1
1 -1  0  0  1  0  0
1  0  1  0  0  0 -1
1  0 -1  0  1  0  0
1  0  0  1  0  0 -1
1  0  0 -1  1  0  0
0 -1 -1 -1  0  1  2
#--------------------------
0 4

N M
Philippe's simple example

#--------------------------
# I have done the work by hand, and here is the right
# answer :
#
# If 1 <= M <= N then EP(N,M) = 1/2 M^2 + 1/2 M
# If N <= M <= 2N-1 then EP(N,M) = -3/2 N^2 - M^2 + 3NM - M
# If 2N-1 <= M <= 3N-2 then EP(N,M) = 9/2 N^2 + 1/2 M^2 - 3NM - 3/2 N + 1/2 M
bash-3.00$ ~/obj/barvinok/barvinok_enumerate < e14.in 
POLYHEDRON Dimension:5
           Constraints:8  Equations:1  Rays:9  Lines:0
Constraints 8 7
Equality:   [   1   1   1   0  -1  -2 ]
Inequality: [   0  -1  -1   0   1   1 ]
Inequality: [   0   1   1   1  -1  -2 ]
Inequality: [   0   1   0   0   0  -1 ]
Inequality: [   0  -1   0   1   0   0 ]
Inequality: [   0   0   1   0   0  -1 ]
Inequality: [   0   0  -1   1   0   0 ]
Inequality: [   0   0   0   0   0   1 ]
Rays 9 7
Ray:    [   1   0   1   1   2 ]
Vertex: [   1   1   1   1   1 ]/1
Ray:    [   0   1   0   1   1 ]
Ray:    [   0   0   0   1   0 ]
Ray:    [   1   0   0   1   1 ]
Ray:    [   1   1   0   1   2 ]
Ray:    [   1   1   1   1   3 ]
Ray:    [   0   1   1   1   2 ]
Ray:    [   0   0   1   1   1 ]
POLYHEDRON Dimension:2
           Constraints:1  Equations:0  Rays:3  Lines:2
Constraints 1 4
Inequality: [   0   0   1 ]
Rays 3 4
Line:   [   1   0 ]
Line:   [   0   1 ]
Vertex: [   0   0 ]/1
         M  -1 >= 0
         N - M  -1 >= 0
          1 >= 0

( 1/2 * M^2 + 1/2 * M + 0 )
         3N - M  -2 >= 0
         -2N + M  >= 0
          1 >= 0

( 9/2 * N^2 + ( -3 * M + -3/2 )
 * N + ( 1/2 * M^2 + 1/2 * M + 0 )
 )
         2N - M  -1 >= 0
         - N + M  >= 0
          1 >= 0

( -3/2 * N^2 + ( 3 * M + 3/2 )
 * N + ( -1 * M^2 + -1 * M + 0 )
 )