Question: how to find whether divisible with ordering for multivariable case

my code can only do for one variable, 

how to make divisible checking for multivariable cases with the ordering such as plex

IsDivisible(LP(h, t), LP(g[i], t), x)

it is not only x when multivariable

f:=LP(y^2*x,plex(x, y))[2];
g:=LP(y*x-y,plex(x, y))[2];
Remainder(f, g, gcd(f,g));
degree(Remainder(f, g, x),x);
degree(g, x);

remainder has error expect its 3rd argument x, to be of type or but received y*x

how to do if have ordering

do it need to check whether both f and g have variable x using indets and then apply remainder?

do it need to check each variable starting from the first variable in the ordering? 

how about if f has variable x but g do not have variable x, or f do not have variable x and g have variable x

if so, i try to replace below code in the bottom code, it has error

Error, (in FindDivisble) cannot determine if this expression is true or false: 0 < Search(x, {x, y})

FindDivisble := proc(g, h, t)
with(ListTools):
result := 0;
for i from 1 to nops(g) do
mainvariable := 0;
for j from 1 to nops(t) do
mainvariable := op(j, t);
if mainvariable <> 0 then
if Search(mainvariable, indets(h)) > 0 and Search(mainvariable, indets(g[i])) > 0 then
if IsDivisible(LP(h,t), LP(g[i],t), mainvariable) = 0 then
return i;
else
result := 0;
end if:
end if:
end if:
od:
od:
return result;
end proc:

with(Groebner):
LP := proc(f, t)
return LeadingTerm(f, t)/LeadingCoefficient(f, t);
end proc:
IsDivisible := proc(f, g, x)
with(Algebraic):
if Remainder(f, g, x) = 0 or degree(Remainder(f, g, x),x) < degree(g, x) then
return 0;
else
return 1;
end if:
end proc:
FindDivisble := proc(g, h, t)
result := 0;
for i from 1 to nops(g) do
if IsDivisible(LP(h, t), LP(g[i], t), x) = 0 then
return i;
else
result := 0;
end if:
od:
return result;
end proc:
MD := proc(f, g, t)
r := 0;
u := Matrix(nops(g), 1);
for j from 1 to nops(g) do
u[j] := 0;
od:
h := f;
while h <> 0 do
i := FindDivisble(g, h, t);
if i > 0 then
u[i] := u[i] + LeadingTerm(h, t)/LeadingTerm(f[i], t);
h := h - LeadingTerm(h, t)/LeadingTerm(f[i], t)*f[i];
else
r := r + LeadingTerm(h, t);
h := h - LeadingTerm(h, t);
end if:
od:
end proc:
f:=y^2*x;
f1 := y*x-y;
f2 := y^2-x;
MD(f,[f1,f2],plex(x, y));