Term Rewriting System R:
[x]
f(s(x)) -> f(g(x, x))
g(0, 1) -> s(0)
0 -> 1

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(s(x)) -> F(g(x, x))
F(s(x)) -> G(x, x)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pair:

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


Rules:


f(s(x)) -> f(g(x, x))
g(0, 1) -> s(0)
0 -> 1


Strategy:

innermost




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

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