  This is a study of the computing power of the subtyping machine behind
Kennedy and Pierce's nominal subtyping with variance. We depict the lattice of
fragments of Kennedy and Pierce's type system and characterize their computing
power in terms of regular, context-free, deterministic, and non-deterministic
tree languages. Based on the theory, we present Treetop -- a generator of C#
implementations of subtyping machines. The software artifact constitutes the
first feasible (yet POC) fluent API generator to support context-free API
protocols in a decidable type system fragment.
