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

Innermost Termination of R to be shown.



   TRS
Reversing
Rev
DPs




Rule(s) before reversing:

f(X) -> g(h(f(X)))


Rule(s) after reversing:

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





Trying another alternative:
   TRS
Rev
Reversing
DPs




Rule(s) before reversing:

f(X) -> g(h(f(X)))


Rule(s) after reversing:

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





Trying another alternative:
   TRS
Rev
Rev
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(X) -> F(X)

Furthermore, R contains one SCC.


   TRS
Rev
Rev
DPs
       →DP Problem 1
Non Termination


Dependency Pair:

F(X) -> F(X)


Rule:


f(X) -> g(h(f(X)))


Strategy:

innermost




Found an infinite P-chain over R:
P =

F(X) -> F(X)

R =

f(X) -> g(h(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:
0:03 minutes