Term Rewriting System R:
[x, y, z]
+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
+'(-(x, y), z) -> -'(+(x, z), y)
+'(-(x, y), z) -> +'(x, z)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
+'(-(x, y), z) -> +'(x, z)
Rules:
+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x
The following dependency pair can be strictly oriented:
+'(-(x, y), z) -> +'(x, z)
Additionally, the following rules can be oriented:
+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(-(x1, x2)) | = 1 + x1 |
| POL(+(x1, x2)) | = x1 |
| POL(+'(x1, x2)) | = x1 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes