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

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(g(x), y, y) -> F(x, x, y)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Argument Filtering and Ordering


Dependency Pair:

F(g(x), y, y) -> F(x, x, y)


Rule:


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





The following dependency pair can be strictly oriented:

F(g(x), y, y) -> F(x, x, y)


There are no usable rules using the Ce-refinement that need to be oriented.
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:
F(x1, x2, x3) -> x1
g(x1) -> g(x1)


   R
DPs
       →DP Problem 1
AFS
           →DP Problem 2
Dependency Graph


Dependency Pair:


Rule:


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





Using the Dependency Graph resulted in no new DP problems.

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