Term Rewriting System R:
[x, y]
f(f(x)) -> f(g(f(x), x))
f(f(x)) -> f(h(f(x), f(x)))
g(x, y) -> y
h(x, x) -> g(x, 0)

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(f(x)) -> F(g(f(x), x))
F(f(x)) -> G(f(x), x)
F(f(x)) -> F(h(f(x), f(x)))
F(f(x)) -> H(f(x), f(x))
H(x, x) -> G(x, 0)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

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


Rules:


f(f(x)) -> f(g(f(x), x))
f(f(x)) -> f(h(f(x), f(x)))
g(x, y) -> y
h(x, x) -> g(x, 0)




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