Term Rewriting System R:
[x, y, z]
+(*(x, y), *(a, y)) -> *(+(x, a), y)
*(*(x, y), z) -> *(x, *(y, z))
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 Pairs:
*'(*(x, y), z) -> *'(y, z)
*'(*(x, y), z) -> *'(x, *(y, z))
Rules:
+(*(x, y), *(a, y)) -> *(+(x, a), y)
*(*(x, y), z) -> *(x, *(y, z))
The following dependency pairs can be strictly oriented:
*'(*(x, y), z) -> *'(y, z)
*'(*(x, y), z) -> *'(x, *(y, z))
The following usable rule w.r.t. to the AFS can be oriented:
*(*(x, y), z) -> *(x, *(y, z))
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
*' > *
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))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes