Term Rewriting System R:
[x, y]
f(a) -> b
f(c) -> d
f(g(x, y)) -> g(f(x), f(y))
f(h(x, y)) -> g(h(y, f(x)), h(x, f(y)))
g(x, x) -> h(e, x)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

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


Rules:


f(a) -> b
f(c) -> d
f(g(x, y)) -> g(f(x), f(y))
f(h(x, y)) -> g(h(y, f(x)), h(x, f(y)))
g(x, x) -> h(e, x)




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