Term Rewriting System R:
[x]
f(a, f(f(a, x), a)) -> f(f(a, f(a, x)), a)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(a, f(f(a, x), a)) -> F(f(a, f(a, x)), a)
F(a, f(f(a, x), a)) -> F(a, f(a, x))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
F(a, f(f(a, x), a)) -> F(a, f(a, x))
Rule:
f(a, f(f(a, x), a)) -> f(f(a, f(a, x)), a)
The following dependency pair can be strictly oriented:
F(a, f(f(a, x), a)) -> F(a, f(a, x))
Additionally, the following usable rule using the Ce-refinement can be oriented:
f(a, f(f(a, x), a)) -> f(f(a, f(a, x)), a)
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(a) | = 0 |
| POL(f(x1, x2)) | = 1 + x1 + x2 |
| POL(F(x1, x2)) | = x1 + x2 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
f(a, f(f(a, x), a)) -> f(f(a, f(a, x)), a)
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:01 minutes