The GKR (Geometric Knowledge Representation) system faces limitations in proving computations that require "backwards" or "sideways" time operations, unlike traditional proving systems. For instance, while normal systems can prove y = sqrt(x) by demonstrating x = y^2, GKR struggles with such transformations without additional data commitments. This limitation also affects its compatibility with SHA256, where GKR's efficiency is notably lower compared to other traditional hashes, such as Poseidon.