Term Rewriting System R:
[X, Y, Z]
f(X) -> cons(X, nf(ng(X)))
f(X) -> nf(X)
g(0) -> s(0)
g(s(X)) -> s(s(g(X)))
g(X) -> ng(X)
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nf(X)) -> f(activate(X))
activate(ng(X)) -> g(activate(X))
activate(X) -> X

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

G(s(X)) -> G(X)
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nf(X)) -> F(activate(X))
ACTIVATE(nf(X)) -> ACTIVATE(X)
ACTIVATE(ng(X)) -> G(activate(X))
ACTIVATE(ng(X)) -> ACTIVATE(X)

Furthermore, R contains three SCCs.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)
       →DP Problem 2
Remaining Obligation(s)
       →DP Problem 3
Remaining Obligation(s)




The following remains to be proven:


   R
DPs
       →DP Problem 1
Remaining Obligation(s)
       →DP Problem 2
Remaining Obligation(s)
       →DP Problem 3
Remaining Obligation(s)




The following remains to be proven:


   R
DPs
       →DP Problem 1
Remaining Obligation(s)
       →DP Problem 2
Remaining Obligation(s)
       →DP Problem 3
Remaining Obligation(s)




The following remains to be proven:

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