/tmp/clpq

yes
| ?- [library('clpqr/examples/eliminat')].
{consulting /freyung/christian/sicstus2.1.9.clp/library/clpqr/examples/eliminat.pl...}
{/freyung/christian/sicstus2.1.9.clp/library/clpqr/examples/eliminat.pl consulted, 200 msec 15600 bytes}

yes
| ?- hull([X,Y]).

{Y=<2},
{X+1/2*Y=<3},
{X>=1},
{Y>=0},
{X+Y>=2} ? 

yes
| ?- example(1,[_,_,X3,X4]).

{X3-1/3*X4>=-1/3},
{X3-11/9*X4=<1/9},
{X3-8/9*X4=<1/9},
{X3-13/18*X4>=-2/9},
{X3-1/6*X4=<1/3} ? 

yes
| ?- example(2,[X0,X1|_]).

{X0+2619277/17854273*X1>=-851123/17854273},
{X0+6429953/16575801*X1=<-12749681/16575801},
{X0+19130/1213083*X1>=795400/404361},
{X0-1251619/3956679*X1>=21101146/3956679},
{X0+601502/4257189*X1>=220850/473021} ? 

yes
| ?- proj(1).
%%% Timing 00:00:00.100     0.100
[A,B,C,D]:6
{B>=0}
{A>=0}
{D-3*C+B+12*A=<1}
{D-9/7*C+1/7*B+18/7*A>=1/7}
{D-18/11*C+2/11*B+36/11*A>=2/11}
{D-18/13*C+4/13*B+45/13*A=<4/13}

%%% Timing 00:00:00.270     0.270
[A,B,C]:6
{A>=0}
{C-6*B-2*A>=-2}
{C-18/13*B+4/13*A=<4/13}
{C-9/11*B-1/11*A>=-1/11}
{C-9/8*B-1/8*A>=-1/8}
{C-3*B+A=<1}

%%% Timing 00:00:00.320     0.320
[A,B]:5
{B-3*A=<1}
{B-9/11*A>=-1/11}
{B-9/8*A>=-1/8}
{B-18/13*A=<4/13}
{B-6*A>=-2}

%%% Timing 00:00:00.290     0.290
[A]:2
{A=<1}
{A>=-1/2}

%%% Timing 00:00:00.030     0.030
[]:0

%%% Timing 00:00:00.260     0.260
[A]:2
{A=<1/2}
{A>=-1/2}

%%% Timing 00:00:00.250     0.250
[A,B]:3
{A>=0}
{B-1/2*A>=-1/2}
{B+A=<1}

%%% Timing 00:00:00.190     0.190
[A]:2
{A>=0}
{A=<1}

%%% Timing 00:00:00.270     0.270
[A,B]:3
{A>=0}
{B-1/2*A>=-1/2}
{B+1/2*A=<1/2}

%%% Timing 00:00:00.260     0.260
[A,B,C]:6
{A>=0}
{C-2*B+3*A>=0}
{C-18/13*B+45/13*A=<4/13}
{C-B+A>=0}
{C-4/3*B+4/3*A>=0}
{C-3*B+12*A=<1}

%%% Timing 00:00:00.250     0.250
[A,B]:4
{A>=0}
{B-36/5*A>=-4/5}
{B-9/2*A>=-1/2}
{B+9/2*A=<1}

%%% Timing 00:00:00.200     0.200
[A]:2
{A>=0}
{A=<2/13}

%%% Timing 00:00:00.230     0.230
[A,B]:4
{A>=0}
{B-32/5*A>=-3/5}
{B-11/2*A>=-1/2}
{B+3/4*A=<1/2}

%%% Timing 00:00:00.230     0.230
[A,B,C]:5
{B>=0}
{A>=0}
{C+B+9/2*A=<1}
{C-1/2*B-9/2*A>=-1/2}
{C-4/5*B-36/5*A>=-4/5}

%%% Timing 00:00:00.200     0.200
[A,B]:3
{B>=0}
{A>=0}
{B+13/2*A=<1}

%%% Timing 00:00:00.210     0.210
[A,B,C]:5
{B>=0}
{A>=0}
{C+1/2*B+3/4*A=<1/2}
{C-1/2*B-11/2*A>=-1/2}
{C-3/5*B-32/5*A>=-3/5}

%%% Timing 00:00:00.000     0.000

no
| ?- proj(3).
%%% Timing 00:00:00.100     0.100
[A,B,C,D]:6
{B>=0}
{A>0}
{D-3*C+B+12*A=<1}
{D-9/7*C+1/7*B+18/7*A>=1/7}
{D-18/11*C+2/11*B+36/11*A>=2/11}
{D-18/13*C+4/13*B+45/13*A=<4/13}

%%% Timing 00:00:00.260     0.260
[A,B,C]:6
{A>=0}
{C-6*B-2*A>=-2}
{C-18/13*B+4/13*A<4/13}
{C-9/11*B-1/11*A>=-1/11}
{C-9/8*B-1/8*A>=-1/8}
{C-3*B+A<1}

%%% Timing 00:00:00.290     0.290
[A,B]:5
{B-3*A<1}
{B-9/11*A>=-1/11}
{B-9/8*A>=-1/8}
{B-18/13*A<4/13}
{B-6*A>=-2}

%%% Timing 00:00:00.280     0.280
[A]:2
{A<1}
{A>-1/2}

%%% Timing 00:00:00.040     0.040
[]:0

%%% Timing 00:00:00.250     0.250
[A]:2
{A<1/2}
{A>-1/2}

%%% Timing 00:00:00.260     0.260
[A,B]:3
{A>=0}
{B-1/2*A>-1/2}
{B+A<1}

%%% Timing 00:00:00.190     0.190
[A]:2
{A>=0}
{A<1}

%%% Timing 00:00:00.260     0.260
[A,B]:3
{A>=0}
{B-1/2*A>-1/2}
{B+1/2*A<1/2}

%%% Timing 00:00:00.260     0.260
[A,B,C]:6
{A>0}
{C-2*B+3*A>=0}
{C-18/13*B+45/13*A=<4/13}
{C-B+A>=0}
{C-4/3*B+4/3*A>=0}
{C-3*B+12*A=<1}

%%% Timing 00:00:00.260     0.260
[A,B]:4
{A>0}
{B-36/5*A>=-4/5}
{B-9/2*A>=-1/2}
{B+9/2*A=<1}

%%% Timing 00:00:00.210     0.210
[A]:2
{A>0}
{A=<2/13}

%%% Timing 00:00:00.230     0.230
[A,B]:4
{A>0}
{B-32/5*A>=-3/5}
{B-11/2*A>=-1/2}
{B+3/4*A=<1/2}

%%% Timing 00:00:00.220     0.220
[A,B,C]:5
{B>=0}
{A>0}
{C+B+9/2*A=<1}
{C-1/2*B-9/2*A>=-1/2}
{C-4/5*B-36/5*A>=-4/5}

%%% Timing 00:00:00.200     0.200
[A,B]:3
{B>=0}
{A>0}
{B+13/2*A=<1}

%%% Timing 00:00:00.230     0.230
[A,B,C]:5
{B>=0}
{A>0}
{C+1/2*B+3/4*A=<1/2}
{C-1/2*B-11/2*A>=-1/2}
{C-3/5*B-32/5*A>=-3/5}

%%% Timing 00:00:00.020     0.020

no
| ?-