Definition 3.6 of [Wo] states that a simplicial complex S is k-decomposable if S is either a simplex or there exists a shedding face F of S of dimension at most k such that both the face deletion and link of S by F are again k-decomposable.
i1 : R = QQ[a..f];
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i2 : isDecomposable(0, simplicialComplex {a*b*c*d*e*f})
o2 = true
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i3 : isDecomposable(2, simplicialComplex {a*b*c, b*c*d, c*d*e})
o3 = true
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The method checks the cache, if possible, to see if the complex is vertex-decomposable.