Term Rewriting System R:
[x]
a(b(a(x))) -> b(a(b(x)))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
A(b(a(x))) -> A(b(x))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
A(b(a(x))) -> A(b(x))
Rule:
a(b(a(x))) -> b(a(b(x)))
The following dependency pair can be strictly oriented:
A(b(a(x))) -> A(b(x))
There are no usable rules w.r.t. to the implicit AFS that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(b(x1)) | = x1 |
| POL(a(x1)) | = 1 + x1 |
| POL(A(x1)) | = 1 + x1 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
a(b(a(x))) -> b(a(b(x)))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes