Term Rewriting System R:
[X, Y, Z]
from(X) -> cons(X, from(s(X)))
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, Z)

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

FROM(X) -> FROM(s(X))
SEL(s(X), cons(Y, Z)) -> SEL(X, Z)

Furthermore, R contains two SCCs.

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

The following remains to be proven:
• Dependency Pair:

FROM(X) -> FROM(s(X))

Rules:

from(X) -> cons(X, from(s(X)))
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, Z)

• Dependency Pair:

SEL(s(X), cons(Y, Z)) -> SEL(X, Z)

Rules:

from(X) -> cons(X, from(s(X)))
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, Z)

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

The following remains to be proven:
• Dependency Pair:

FROM(X) -> FROM(s(X))

Rules:

from(X) -> cons(X, from(s(X)))
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, Z)

• Dependency Pair:

SEL(s(X), cons(Y, Z)) -> SEL(X, Z)

Rules:

from(X) -> cons(X, from(s(X)))
sel(0, cons(X, Y)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, Z)

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