Term Rewriting System R:
[y, n, x]
app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

APP(add(n, x), y) -> APP(x, y)

Furthermore, R contains three SCCs.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`
`       →DP Problem 2`
`         ↳Remaining Obligation(s)`
`       →DP Problem 3`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
• Dependency Pair:

APP(add(n, x), y) -> APP(x, y)

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

• Dependency Pair:

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

• Dependency Pair:

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`
`       →DP Problem 2`
`         ↳Remaining Obligation(s)`
`       →DP Problem 3`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
• Dependency Pair:

APP(add(n, x), y) -> APP(x, y)

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

• Dependency Pair:

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

• Dependency Pair:

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`
`       →DP Problem 2`
`         ↳Remaining Obligation(s)`
`       →DP Problem 3`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
• Dependency Pair:

APP(add(n, x), y) -> APP(x, y)

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

• Dependency Pair:

Rules:

app(nil, y) -> y
reverse(nil) -> nil
shuffle(nil) -> nil

• Dependency Pair:

Rules:

app(nil, y) -> y