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

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

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


Rules:


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




Termination of R could not be shown.
Duration:
0:00 minutes