Term Rewriting System R:
[x]
f(f(x)) -> f(c(f(x)))
f(f(x)) -> f(d(f(x)))
g(c(x)) -> x
g(d(x)) -> x
g(c(h(0))) -> g(d(1))
g(c(1)) -> g(d(h(0)))
g(h(x)) -> g(x)

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(f(x)) -> F(c(f(x)))
F(f(x)) -> F(d(f(x)))
G(c(h(0))) -> G(d(1))
G(c(1)) -> G(d(h(0)))
G(h(x)) -> G(x)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pair:

G(h(x)) -> G(x)


Rules:


f(f(x)) -> f(c(f(x)))
f(f(x)) -> f(d(f(x)))
g(c(x)) -> x
g(d(x)) -> x
g(c(h(0))) -> g(d(1))
g(c(1)) -> g(d(h(0)))
g(h(x)) -> g(x)




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