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This paper contributes to the theory and practice of automatic extraction of synchronization-free parallelism in nested loops. It extends the iteration-space slicing framework to extract slices described by not only affine (linear) but also non-affine forms. A slice is represented by a set of dependent loop statement instances (iterations) forming an arbitrary graph topology. The algorithm generates an outer loop to spawn synchronization-free slices to be executed in parallel, enclosing sequential loops iterating over those slices. Experimental results demonstrate that the generated code is competitive with that generated by state-of-the-art techniques scanning polyhedra.