Term Rewriting System R:
[x]
f(f(a, x), a) -> f(f(x, f(a, a)), a)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(f(a, x), a) -> F(f(x, f(a, a)), a)
F(f(a, x), a) -> F(x, f(a, a))
F(f(a, x), a) -> F(a, a)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pairs:
F(f(a, x), a) -> F(x, f(a, a))
F(f(a, x), a) -> F(f(x, f(a, a)), a)
Rule:
f(f(a, x), a) -> f(f(x, f(a, a)), a)
The following dependency pair can be strictly oriented:
F(f(a, x), a) -> F(x, f(a, a))
Additionally, the following usable rule using the Ce-refinement can be oriented:
f(f(a, x), a) -> f(f(x, f(a, a)), a)
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(a) | = 1 |
| POL(f(x1, x2)) | = 0 |
| POL(F(x1, x2)) | = x2 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pair:
F(f(a, x), a) -> F(f(x, f(a, a)), a)
Rule:
f(f(a, x), a) -> f(f(x, f(a, a)), a)
Termination of R could not be shown.
Duration:
0:00 minutes