Maxima cannot deduce obvious facts which follow from the transitivity of the inequality operator.
(%i) assume(x > y)
(%o) [x > y]
(%i) assume(x > 1)
(%o) [x > 1]
(%i) is(x^2 > x)
(%o) true
(%i) is(x^2 > y)
(%o) unknown
I have created the operators '>>' and '<<' to overcome this weakness. They work by creating a digraph G whose vertices are the arguments of the relevant (in)equalities in the assume database, with edges between vertices if one is less than the other. The predicate is then equivalent to reachability in the digraph.
(%i) x^2 >> y
(%o) true
To see the graph generated by using the operators, enter dg(G).
(%i) dg(G);
(%o) done
