Example. A finite delegated run and its lineage cost [ftip-00CL]
Example. A finite delegated run and its lineage cost [ftip-00CL]
Use two cost coordinates, such as output tokens and tool calls. The root delegates to two children, and one child delegates once more.
The cost of a child subtree is its local cost plus the costs of all descendants. Therefore
\[ C_{\rm lin}(\mathcal T)=c_r+C_{\rm lin}(\mathcal T_a)+C_{\rm lin}(\mathcal T_b). \]Charging only the root hides descendant work; charging a descendant again as a separate parent-local cost double counts it.