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
↳Argument Filtering and Ordering
Dependency Pair:
*'(x, *(minus(y), y)) -> *'(minus(*(y, y)), x)
Rule:
*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)
Strategy:
innermost
The following dependency pair can be strictly oriented:
*'(x, *(minus(y), y)) -> *'(minus(*(y, y)), x)
The following usable rule for innermost can be oriented:
*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(*'(x1, x2)) | = x1 + x2 |
| POL(*(x1, x2)) | = 1 + x1 + x2 |
| POL(minus) | = 0 |
resulting in one new DP problem.
Used Argument Filtering System: *'(x1, x2) -> *'(x1, x2)
*(x1, x2) -> *(x1, x2)
minus(x1) -> minus
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes