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

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pair:

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


Rules:


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




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