Term Rewriting System R:
[X, XS, N]
from(X) -> cons(X, from(s(X)))
head(cons(X, XS)) -> X
2nd(cons(X, XS)) -> head(XS)
take(0, XS) -> nil
take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
sel(0, cons(X, XS)) -> X
sel(s(N), cons(X, XS)) -> sel(N, XS)

Innermost Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

FROM(X) -> FROM(s(X))
2ND(cons(X, XS)) -> HEAD(XS)
TAKE(s(N), cons(X, XS)) -> TAKE(N, XS)
SEL(s(N), cons(X, XS)) -> SEL(N, XS)

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:

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