Term Rewriting System R:
[x]
f(a, f(a, x)) -> f(a, f(x, f(f(a, a), a)))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(a, f(a, x)) -> F(a, f(x, f(f(a, a), a)))
F(a, f(a, x)) -> F(x, f(f(a, a), a))
F(a, f(a, x)) -> F(f(a, a), a)
F(a, f(a, x)) -> F(a, a)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Semantic Labelling
Dependency Pair:
F(a, f(a, x)) -> F(a, f(x, f(f(a, a), a)))
Rule:
f(a, f(a, x)) -> f(a, f(x, f(f(a, a), a)))
Using Semantic Labelling, the DP problem could be transformed. The following model was found:
| f(x0, x1) | = 0 |
| a | = 1 |
| F(x0, x1) | = 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