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

Innermost Termination of R to be shown.



   TRS
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(x) -> F(f(x))
F(x) -> F(x)

Furthermore, R contains one SCC.


   TRS
DPs
       →DP Problem 1
Non Termination


Dependency Pairs:

F(x) -> F(x)
F(x) -> F(f(x))


Rule:


f(x) -> f(f(x))


Strategy:

innermost




Found an infinite P-chain over R:
P =

F(x) -> F(x)
F(x) -> F(f(x))

R =

f(x) -> f(f(x))

s = F(x')
evaluates to t =F(x')

Thus, s starts an infinite chain.

Innermost Non-Termination of R could be shown.
Duration:
0:00 minutes