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

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

+'(*(x, y), *(a, y)) -> *'(+(x, a), y)
+'(*(x, y), *(a, y)) -> +'(x, a)
*'(*(x, y), z) -> *'(x, *(y, z))
*'(*(x, y), z) -> *'(y, z)

Furthermore, R contains one SCC.

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

Dependency Pair:

*'(*(x, y), z) -> *'(y, z)

Rules:

+(*(x, y), *(a, y)) -> *(+(x, a), y)
*(*(x, y), z) -> *(x, *(y, z))

Strategy:

innermost

The following dependency pair can be strictly oriented:

*'(*(x, y), z) -> *'(y, z)

There are no usable rules for innermost that need to be oriented.
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:
*'(x1, x2) -> *'(x1, x2)
*(x1, x2) -> *(x1, x2)

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

Dependency Pair:

Rules:

+(*(x, y), *(a, y)) -> *(+(x, a), y)
*(*(x, y), z) -> *(x, *(y, z))

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

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