Term Rewriting System R:
[X, Y]
from(X) -> cons(X, from(s(X)))
length(nil) -> 0
length(cons(X, Y)) -> s(length1(Y))
length1(X) -> length(X)
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
FROM(X) -> FROM(s(X))
LENGTH(cons(X, Y)) -> LENGTH1(Y)
LENGTH1(X) -> LENGTH(X)
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)))
length(nil) -> 0
length(cons(X, Y)) -> s(length1(Y))
length1(X) -> length(X)
Strategy:
innermost
As we are in the innermost case, we can delete all 4 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