Term Rewriting System R:
[x, y, z]
f(g(x), h(x), y, x) -> f(y, y, y, x)
f(x, y, z, 0) -> 2
g(0) -> 2
h(0) -> 2

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Forward Instantiation Transformation


Dependency Pair:

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


Rules:


f(g(x), h(x), y, x) -> f(y, y, y, x)
f(x, y, z, 0) -> 2
g(0) -> 2
h(0) -> 2





On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

F(g(x), h(x), y, x) -> F(y, y, y, x)
no new Dependency Pairs are created.
The transformation is resulting in no new DP problems.


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