Term Rewriting System R:
[x]
f(f(x, a), a) -> f(f(f(a, a), f(x, a)), a)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(f(x, a), a) -> F(f(f(a, a), f(x, a)), a)
F(f(x, a), a) -> F(f(a, a), f(x, a))
F(f(x, a), a) -> F(a, a)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Semantic Labelling
Dependency Pair:
F(f(x, a), a) -> F(f(f(a, a), f(x, a)), a)
Rule:
f(f(x, a), a) -> f(f(f(a, a), f(x, a)), a)
Using Semantic Labelling, the DP problem could be transformed. The following model was found:
| F(x0, x1) | = 1 |
| f(x0, x1) | = 0 |
| a | = 1 |
From the dependency graph we obtain 0 (labeled) SCCs which each result in correspondingDP problem.
Termination of R successfully shown.
Duration:
0:00 minutes