Term Rewriting System R:
[x, y]
-(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(-(x, y), -(x, y))
-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(x, y)

Furthermore, R contains one SCC.

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

Dependency Pairs:

-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(x, y)
-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(-(x, y), -(x, y))

Rule:

-(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))

The following dependency pairs can be strictly oriented:

-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(x, y)
-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(-(x, y), -(x, y))

The following usable rule w.r.t. to the AFS can be oriented:

-(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))

Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:
-'(x1, x2) -> x1
-(x1, x2) -> x1
neg(x1) -> neg(x1)

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

Dependency Pair:

Rule:

-(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))

Using the Dependency Graph resulted in no new DP problems.

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