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

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Usable Rules (Innermost)`

Dependency Pair:

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

Rule:

*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)

Strategy:

innermost

As we are in the innermost case, we can delete all 1 non-usable-rules.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳UsableRules`
`           →DP Problem 2`
`             ↳Size-Change Principle`

Dependency Pair:

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

Rule:

none

Strategy:

innermost

We number the DPs as follows:
1. *'(x, *(minus(y), y)) -> *'(minus(*(y, y)), x)
and get the following Size-Change Graph(s):
{1} , {1}
1=2
2>1

which lead(s) to this/these maximal multigraph(s):
{1} , {1}
1>1
2>2

DP: empty set
Oriented Rules: none

We used the order Homeomorphic Embedding Order with Non-Strict Precedence.
trivial

with Argument Filtering System:
minus(x1) -> minus
*(x1, x2) -> *(x1, x2)

We obtain no new DP problems.

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