Term Rewriting System R:
[x]
f(f(a, f(x, a)), a) -> f(a, f(f(x, a), a))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(f(a, f(x, a)), a) -> F(a, f(f(x, a), a))
F(f(a, f(x, a)), a) -> F(f(x, a), a)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
F(f(a, f(x, a)), a) -> F(f(x, a), a)
Rule:
f(f(a, f(x, a)), a) -> f(a, f(f(x, a), a))
The following dependency pair can be strictly oriented:
F(f(a, f(x, a)), a) -> F(f(x, a), a)
The following usable rule using the Ce-refinement can be oriented:
f(f(a, f(x, a)), a) -> f(a, f(f(x, a), a))
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(a) | = 0 |
| POL(F(x1, x2)) | = 1 + x1 + x2 |
| POL(f(x1, x2)) | = 1 + x1 + x2 |
resulting in one new DP problem.
Used Argument Filtering System: F(x1, x2) -> F(x1, x2)
f(x1, x2) -> f(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
f(f(a, f(x, a)), a) -> f(a, f(f(x, a), a))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes