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)
Innermost 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
↳Usable Rules (Innermost)
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)
Strategy:
innermost
As we are in the innermost case, we can delete all 3 non-usable-rules.
R
↳DPs
→DP Problem 1
↳UsableRules
→DP Problem 3
↳Non Termination
Dependency Pair:
FROM(X) -> FROM(s(X))
Rule:
none
Strategy:
innermost
Found an infinite P-chain over R:
P =
FROM(X) -> FROM(s(X))
R = none
s = FROM(X)
evaluates to t =FROM(s(X))
Thus, s starts an infinite chain as s matches t.
Innermost Non-Termination of R could be shown.
Duration:
0:01 minutes