Term Rewriting System R:
[x, y, z]
*(x, +(y, z)) -> +(*(x, y), *(x, z))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
*'(x, +(y, z)) -> *'(x, y)
*'(x, +(y, z)) -> *'(x, z)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pairs:
*'(x, +(y, z)) -> *'(x, z)
*'(x, +(y, z)) -> *'(x, y)
Rule:
*(x, +(y, z)) -> +(*(x, y), *(x, z))
The following dependency pairs can be strictly oriented:
*'(x, +(y, z)) -> *'(x, z)
*'(x, +(y, z)) -> *'(x, y)
The following rule can be oriented:
*(x, +(y, z)) -> +(*(x, y), *(x, z))
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)
*(x1, x2) -> x2
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
*(x, +(y, z)) -> +(*(x, y), *(x, z))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes