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

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Semantic Labelling


Dependency Pair:

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


Rule:


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





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