Term Rewriting System R:
[x, y]
f(a) -> g(h(a))
h(g(x)) -> g(h(f(x)))
k(x, h(x), a) -> h(x)
k(f(x), y, x) -> f(x)

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pair:

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


Rules:


f(a) -> g(h(a))
h(g(x)) -> g(h(f(x)))
k(x, h(x), a) -> h(x)
k(f(x), y, x) -> f(x)




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