Term Rewriting System R:
[x, y, z]
app(app(., 1), x) -> x
app(app(., x), 1) -> x
app(app(., app(i, x)), x) -> 1
app(app(., x), app(i, x)) -> 1
app(app(., app(i, y)), app(app(., y), z)) -> z
app(app(., y), app(app(., app(i, y)), z)) -> z
app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z))
app(i, 1) -> 1
app(i, app(i, x)) -> x
app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

APP(app(., app(app(., x), y)), z) -> APP(app(., x), app(app(., y), z))
APP(app(., app(app(., x), y)), z) -> APP(app(., y), z)
APP(app(., app(app(., x), y)), z) -> APP(., y)
APP(i, app(app(., x), y)) -> APP(app(., app(i, y)), app(i, x))
APP(i, app(app(., x), y)) -> APP(., app(i, y))
APP(i, app(app(., x), y)) -> APP(i, y)
APP(i, app(app(., x), y)) -> APP(i, x)

Furthermore, R contains one SCC.

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

The following remains to be proven:
Dependency Pairs:

APP(i, app(app(., x), y)) -> APP(i, x)
APP(i, app(app(., x), y)) -> APP(i, y)
APP(i, app(app(., x), y)) -> APP(app(., app(i, y)), app(i, x))
APP(app(., app(app(., x), y)), z) -> APP(app(., y), z)
APP(app(., app(app(., x), y)), z) -> APP(app(., x), app(app(., y), z))

Rules:

app(app(., 1), x) -> x
app(app(., x), 1) -> x
app(app(., app(i, x)), x) -> 1
app(app(., x), app(i, x)) -> 1
app(app(., app(i, y)), app(app(., y), z)) -> z
app(app(., y), app(app(., app(i, y)), z)) -> z
app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z))
app(i, 1) -> 1
app(i, app(i, x)) -> x
app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x))

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