Term Rewriting System R:
[x, y, z]
*(i(x), x) -> 1
*(1, y) -> y
*(x, 0) -> 0
*(*(x, y), z) -> *(x, *(y, z))
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
*'(*(x, y), z) -> *'(x, *(y, z))
*'(*(x, y), z) -> *'(y, z)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
*'(*(x, y), z) -> *'(y, z)
Rules:
*(i(x), x) -> 1
*(1, y) -> y
*(x, 0) -> 0
*(*(x, y), z) -> *(x, *(y, z))
Strategy:
innermost
The following dependency pair can be strictly oriented:
*'(*(x, y), z) -> *'(y, z)
There are no usable rules for innermost w.r.t. to the implicit AFS that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(*'(x1, x2)) | = x1 |
| POL(*(x1, x2)) | = 1 + x2 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
*(i(x), x) -> 1
*(1, y) -> y
*(x, 0) -> 0
*(*(x, y), z) -> *(x, *(y, z))
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes