Term Rewriting System R:
[x, y]
rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

REV(++(x, y)) -> REV(y)
REV(++(x, y)) -> REV(x)
REV(++(x, x)) -> REV(x)

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Argument Filtering and Ordering`

Dependency Pairs:

REV(++(x, x)) -> REV(x)
REV(++(x, y)) -> REV(x)
REV(++(x, y)) -> REV(y)

Rules:

rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

The following dependency pairs can be strictly oriented:

REV(++(x, x)) -> REV(x)
REV(++(x, y)) -> REV(x)
REV(++(x, y)) -> REV(y)

There are no usable rules w.r.t. to the AFS that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
 POL(REV(x1)) =  1 + x1 POL(++(x1, x2)) =  1 + x1 + x2

resulting in one new DP problem.
Used Argument Filtering System:
REV(x1) -> REV(x1)
++(x1, x2) -> ++(x1, x2)

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳AFS`
`           →DP Problem 2`
`             ↳Dependency Graph`

Dependency Pair:

Rules:

rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

Using the Dependency Graph resulted in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes