Term Rewriting System R:
[x]
f(a, f(x, a)) -> f(a, f(f(a, a), x))
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(a, f(x, a)) -> F(a, f(f(a, a), x))
F(a, f(x, a)) -> F(f(a, a), x)
F(a, f(x, a)) -> F(a, a)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pairs:
F(a, f(x, a)) -> F(f(a, a), x)
F(a, f(x, a)) -> F(a, f(f(a, a), x))
Rule:
f(a, f(x, a)) -> f(a, f(f(a, a), x))
Strategy:
innermost
The following dependency pair can be strictly oriented:
F(a, f(x, a)) -> F(f(a, a), x)
Additionally, the following usable rule for innermost can be oriented:
f(a, f(x, a)) -> f(a, f(f(a, a), x))
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(a) | = 1 |
| POL(f(x1, x2)) | = 0 |
| POL(F(x1, x2)) | = x1 |
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(a, f(x, a)) -> F(a, f(f(a, a), x))
Rule:
f(a, f(x, a)) -> f(a, f(f(a, a), x))
Strategy:
innermost
Innermost Termination of R could not be shown.
Duration:
0:00 minutes