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

Termination of R to be shown. 



   TRS
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

C -> F(g(c))
C -> C

Furthermore, R contains one SCC. 


   TRS
     ↳DPs
       →DP Problem 1
         ↳Non Termination


Dependency Pair:

C -> C


Rules:


c -> f(g(c))
f(g(X)) -> g(X)





Found an infinite P-chain over R:
P =

C -> C

R =

c -> f(g(c))
f(g(X)) -> g(X)

s = C
evaluates to t =C

Thus, s starts an infinite chain.

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