There have been studies that analyse and apply input space partitioning by categorising them into classes such as equivalence partitioning, boundary value testing, category partitions, domain testing, classification trees, etc. This paper proposes a new algorithm for automated input domain modeling with randomised test case generation in a classification tree adhering to some Lie-algebraic structures using a scalable parallelised framework of second-order cellular automata that encompasses a large number of test cases simultaneously. As a proof of concept, this computational system is compared to a physical system described by a Yang-Mills theory of hypothetical quanta of certain gauge-invariant fields that follow the symmetries followed by the Lie algebras considered, in the foreground of the chaotic system as a continuum limit of the cellular automata, and the test cases are compared to the corresponding Feynman diagrams. Brief complexity analyses and brief analogies between the proof and the Feynman diagrammatics, algebraic complexity theory, and finite difference methods have also discussed.