@Carl Love Many thanks.  As usual I am impressed with the solutions.  Many thanks to @Kitonum too.

I believe that you know, by now, what kind of problem I am dealing with, that is, a set of  full quadratic models with coefficients thetas (30 in total), model=[f(x,y,z),g(x,y,z),h(x,y,z)]. Per chance, would you know to create all the  models with a specific monomial in it (I hope I have used the right term)? For instance, the model used in this thread has the monomial x*y*theta[5] in it.  Taking as the starting point the full quadratic model, how many models can one find with the aforementioned monomial?   Bulding all of them does not seem a good idea, 2ˆ30-1.  

@Kitonum Many thanks.  It works.

@Carl Love  Here is the error.  

Error, cyclic dependency detected in parameter V::(depends(And(list(name), satisfies(proc (V) options operator, arrow; nops(V) = nops(F) end proc)))) in procedure MyTest

@Kitonum Many many thanks.  I completely forgot about depends.  

@Carl Love Many thanks for the procedure. Unfortunately it returns a cyclic error on Maple 14.   What is the precisely mathematicsal term to be used, please? (I am not trying to be funny or else)

@acer Many many thanks.   I will try to see if I can understand what Maplets is all about.  

@acer Many many thanks.  Not do I have a progressslider but also to save my own packages. 

I would appreciate if you could find a way to get it working in Maple 14.  I need to know where my proc got stuck after the 30 GB of ram ran out.   

@acer  Many thanks.   It works just fine.   Could that be part of a package?   A similar function that works on Maple 14 would be great. Many thanks.

@emendes I must be dumb! I could not reproduce the example given on examples,ProgrammaticContentGeneration on a clean worksheet. I do not know where the icon just before ProgressBar comes from.  I am completely lost.  

@acer Many thanks.   The shipbuilding sounds good since Maple 14 is the version I am using for the heavy calculation.  The function I want to monitor is inside of a module (which eventually will be a package saved with savelib).  

Yes, the update needs to be updated only modulo some large-ish number chosen depending on the size of the loop.

@Carl Love Many thanks.  Just of the sake of posting the concise version, here it is 

Test1:=(f::list(algebraic),vars::list(name))-> not evalb(member(true,zip((w,v)-> ((depends(w,v) and not depends(w,remove(has,vars,v))) or not depends(w,vars)),f,vars))):

@Carl Love Many thanks, Carl.   At least I am happy that I could work out a solution (of course based on Kitonum's first reply).  Your function, which is far more concise than mine, returns the same results.  Those are the kind of results I need.  I thank Kitonum too.

@emendes Sorry for the some many replies.   Another attempt

Test:=proc(f::list,vars::list)

local flag,sol:

flag:=member(true,zip((w,v)-> ((depends(w,v) and not depends(w,remove(has,vars,v))) or not depends(w,vars)),f,vars));

sol:=`if`(flag,false,true):

return(sol):

end proc:

@emendes The following procedure seems to work except for the case where the input is ffff.

Test:=proc(f::list,vars::list)

local flag,sol:

flag:=member(true,zip((w,v)-> (depends(w,v) and not depends(w,remove(has,vars,v))),f,vars));

sol:=`if`(flag,false,true):

end proc:

@emendes Sorry, somehow I haven't noticed the other tests within if.  Is there to build a more concise test? Many thanks.