  In this paper we propose a combinatorial framework to study a diagrammatic
representation of the affine Temperley-Lieb algebra of type C introduced by
Ernst. In doing this, we define two procedures, a decoration algorithm on
diagrams and a reduction algorithm on heaps of independent interest. Using this
approach, an explicit algorithmic description of Ernst representation map is
provided from which its faithfulness can be deduced. We also give a
construction of the inverse map.
