---
description: >-
  DUEL and xDUEL are distinct tokens with a structured redemption process: upon
  completion, one token is burned while its counterpart is minted.
---

# Token Redemption

**Converting DUEL to xDUEL:** DUEL can be converted for xDUEL instantly without penalties. The conversion ratio is consistently 1:1 (100%).

**Redeeming xDUEL to DUEL:** Redeeming xDUEL for DUEL involves an unlock period chosen by the user. The conversion ratio varies based on the duration selected:

* Minimum redemption duration of **15 days** yields a ratio of 1:0.25 (25%). 75% of xDUEL is burned upon redemption.
* Medium redemption duration of **45 days** yields a ratio of 1:0.625 (62.5%). 37.5% of xDUEL is burned.
* Maximum redemption duration of **90 days** offers a 1:1 ratio (100%).

### Redemption Ratio Based on Redemption Duration:

$$
\begin{equation}
\begin{aligned}
    & \textbf{Conversion:} \\
    & xDUEL = DUEL \\
    \\
    & \textbf{Redemption:} \\
    & \frac{DUEL_{\text{redeemed}}}{xDUEL_{\text{redeemed}}} = \begin{cases} 
    \frac{1}{4} & \text{for } t_{\text{min}} = 15 \text{ days} \\
    \frac{5}{8} & \text{for } t_{\text{med}} = 45 \text{ days} \\
    1 & \text{for } t_{\text{max}} = 90 \text{ days} 
    \end{cases}
\end{aligned}
\end{equation}
$$

$$
\begin{equation}
\begin{aligned}
    \\
    & \textbf{Token Burn Calculation:} \\
    & xDUEL_{\text{burned}} = xDUEL_{\text{issued}} - \frac{DUEL_{\text{redeemed}}}{\text{Conversion Ratio}} \\
\end{aligned}
\end{equation}
$$

### Circulating Supply Reduction

When users redeem xDUEL tokens, they can choose from various redemption durations, which affect the amount of DUEL tokens they receive. The remaining xDUEL tokens that are not redeemed in full are forfeited, resulting in the following:

$$
\begin{equation}
\begin{aligned}
    & \textbf{Token Burn and Circulation Reduction Mechanism:} \\
    & xDUEL_{\text{burned}} = xDUEL_{\text{issued}} - \left( \text{Conversion Ratio} \times DUEL_{\text{redeemed}} \right) \\
    & DUEL_{\text{burned}} = xDUEL_{\text{burned}} \times \text{Conversion Ratio} \\
    & DUEL_{\text{removed}} = DUEL_{\text{burned}}
\end{aligned}
\end{equation}
$$

This systematic burning of tokens ensures that the total supply of DUEL tokens remains deflationary, supporting a controlled and transparent token economy.

Users have the flexibility to cancel the redemption process at any time, even after the unlock period, with the entire amount of xDUEL returned but no DUEL issued. Cancelling a redemption resets the unlock period for any subsequent redemption attempts.







