Term Rewriting System R:
[x, y]
app(app(times, x), 0) -> 0
app(app(times, x), app(s, y)) -> app(app(plus, app(app(times, x), y)), x)
app(app(plus, x), 0) -> x
app(app(plus, 0), x) -> x
app(app(plus, x), app(s, y)) -> app(s, app(app(plus, x), y))
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

APP(app(times, x), app(s, y)) -> APP(app(plus, app(app(times, x), y)), x)
APP(app(times, x), app(s, y)) -> APP(plus, app(app(times, x), y))
APP(app(times, x), app(s, y)) -> APP(app(times, x), y)
APP(app(plus, x), app(s, y)) -> APP(s, app(app(plus, x), y))
APP(app(plus, x), app(s, y)) -> APP(app(plus, x), y)
APP(app(plus, app(s, x)), y) -> APP(s, app(app(plus, x), y))
APP(app(plus, app(s, x)), y) -> APP(app(plus, x), y)
APP(app(plus, app(s, x)), y) -> APP(plus, x)

Furthermore, R contains one SCC.

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

The following remains to be proven:
Dependency Pairs:

APP(app(plus, app(s, x)), y) -> APP(app(plus, x), y)
APP(app(plus, x), app(s, y)) -> APP(app(plus, x), y)
APP(app(times, x), app(s, y)) -> APP(app(times, x), y)
APP(app(times, x), app(s, y)) -> APP(app(plus, app(app(times, x), y)), x)

Rules:

app(app(times, x), 0) -> 0
app(app(times, x), app(s, y)) -> app(app(plus, app(app(times, x), y)), x)
app(app(plus, x), 0) -> x
app(app(plus, 0), x) -> x
app(app(plus, x), app(s, y)) -> app(s, app(app(plus, x), y))
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))

Termination of R could not be shown.
Duration:
0:00 minutes