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
Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Narrowing Transformation


Dependency Pair:

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


Rules:


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


Strategy:

innermost




On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

H(f(f(x))) -> H(f(g(f(x))))
one new Dependency Pair is created:

H(f(f(x''))) -> H(f(f(x'')))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
Nar
           →DP Problem 2
Remaining Obligation(s)




The following remains to be proven:
Dependency Pair:

H(f(f(x''))) -> H(f(f(x'')))


Rules:


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


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:00 minutes