Term Rewriting System R:

   [x]
   h(f(f(x))) -> h(f(g(f(x))))
   f(g(f(x))) -> f(f(x))

Innermost Termination of R to be shown.


R contains the following Dependency Pairs: 


   F(g(f(x))) -> F(f(x))
   H(f(f(x))) -> H(f(g(f(x))))
   H(f(f(x))) -> F(g(f(x)))

Furthermore, R contains one SCC.


SCC1:

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

Found an infinite P-chain over R:
P = H(f(f(x))) -> H(f(g(f(x))))
R = [f(g(f(x))) -> f(f(x))]
s = H(f(f(x'''))) evaluates to t = H(f(f(x''')))
Thus, s starts an infinite reduction.


Innermost Non-Termination of R could be shown.

Duration: 1.106 seconds.