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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(a, h(x)) -> F(g(x), h(x))
F(a, h(x)) -> G(x)
H(g(x)) -> H(a)
G(h(x)) -> G(x)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pair:

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


Rules:


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


Strategy:

innermost




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

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


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