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

Termination of R to be shown.



   TRS
Reversing
Rev
DPs




Rule(s) before reversing:

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


Rule(s) after reversing:

f'(x) -> g'(f'(x))





Trying another alternative:
   TRS
Rev
Reversing
DPs




Rule(s) before reversing:

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


Rule(s) after reversing:

f'(x) -> g'(f'(x))





Trying another alternative:
   TRS
Rev
Rev
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(x) -> F(g(x))

Furthermore, R contains one SCC.


   TRS
Rev
Rev
DPs
       →DP Problem 1
Non Termination


Dependency Pair:

F(x) -> F(g(x))


Rule:


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





Found an infinite P-chain over R:
P =

F(x) -> F(g(x))

R =

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

s = F(x)
evaluates to t =F(g(x))

Thus, s starts an infinite chain as s matches t.

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