Define BI(m) -- build the polynomial corresponding to the interval [1,log(m)]
  TopLevel CurrentRing;
  N:=NumIndets(CurrentRing);
  L1:=indets(CurrentRing);
 Images:=NewList(N);
  For i:=1 To N Do
    Images[i]:=L1[i]+1;
  EndFor;
  phi := PolyAlgebraHom(CurrentRing,CurrentRing , Images);
G := support(phi(m));
Return sum(G) ;
EndDefine; --BI

-- 1) M = m, n =5
N:=5;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5];
s:=3;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 2) M = m, n = 6
N:=6;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6];
s:=4;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 3) M = m, n = 7
N:=7;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7];
s:=4;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 4) M = m, n = 8	  
N:=8;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7]*x[8];
s:=4;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 5) M = m,  n = 9
N:=9;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7]*x[8]*x[9];
s:=5;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 6) M = m, n = 10	  
N:=10;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7]*x[8]*x[9]*x[10];
s:=5;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 7) M = m, n = 11
N:=11;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7]*x[8]*x[9]*x[10]*x[11];
s:=6;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 8) M = m, n = 12
N:=12;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7]*x[8]*x[9]*x[10]*x[11]*x[12];
s:=6;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 9) M = m, n = 13
N:=13;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7]*x[8]*x[9]*x[10]*x[11]*x[12]*x[13];
s:=7;
P:=BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0)

-- 10) M = R^2 + m, n = 4
N:=4;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4];
s:=3;
P:=3*BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);

-- 11) M = R + m, n = 6
N:=6;
Use S::=QQ[x[1..N]];
g:=x[1]*x[2]*x[3]*x[4]*x[5]*x[6];
s:=4;
P:=2*BI(g)-1;
t0:=CpuTime();
Start(g,s,P);
PrintLn "Time: ",DecimalStr(CpuTime()-t0);