Term Rewriting System R:
[x]
f(a, f(a, x)) -> f(a, f(f(a, x), f(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(f(a, x), f(a, a)))
F(a, f(a, x)) -> F(f(a, x), f(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(f(a, x), f(a, a)))


Rule:


f(a, f(a, x)) -> f(a, f(f(a, x), f(a, a)))





Using Semantic Labelling, the DP problem could be transformed. The following model was found:
F(x0, x1)=  1
a=  1
f(x0, x1)=  0

From the dependency graph we obtain 0 (labeled) SCCs which each result in correspondingDP problem.

Termination of R successfully shown.
Duration:
0:00 minutes