# Gas Cost Analysis

## Aggregation Cost

The cost of verifying aggregated user proofs in a Gnark Groth16 super-proof system can be broken down as follows:

Base cost:

`354,241 Gas`

for verifying the super-proof on-chain.Per-proof cost:

`~6,200 Gas`

for processing and state updates per individual proof aggregated.

The gas cost formula for aggregation per proof turns out to be:

## Verification Access Cost

Users can verify that a certain zk-proof, corresponding to specific public inputs, is included in the superproof. This verification is done through a cross-contract call, as described in the integration docs. The gas cost for this verification process is approximately 7,300 Gas per call.

## Total Cost Per Proof

The total cost of verifying each proof in an aggregated system consists of two components:

Fixed Cost:

`13,500(6200+7300) Gas`

This cost remains constant per proof, regardless of the number of proofs aggregated.Diminishing Cost:

`(354,241 / n) Gas`

Where n is the number of proofs aggregated in a single superproof. This cost decreases as the number of aggregated proofs increases.

Key Point: The Diminishing Cost represents an economy of scale – the more proofs aggregated into a single superproof, the lower the per-proof cost for this component.

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