Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
from(X) |
→ cons(X,from(s(X))) |
| 2: |
|
length(nil) |
→ 0 |
| 3: |
|
length(cons(X,Y)) |
→ s(length1(Y)) |
| 4: |
|
length1(X) |
→ length(X) |
|
There are 3 dependency pairs:
|
| 5: |
|
FROM(X) |
→ FROM(s(X)) |
| 6: |
|
LENGTH(cons(X,Y)) |
→ LENGTH1(Y) |
| 7: |
|
LENGTH1(X) |
→ LENGTH(X) |
|
The approximated dependency graph contains 2 SCCs:
{5}
and {6,7}.
-
Consider the SCC {5}.
There are no usable rules.
The constraints could not be solved.
-
Consider the SCC {6,7}.
There are no usable rules.
By taking the AF π with
π(LENGTH) = π(LENGTH1) = 1
and π(cons) = [2] together with
the lexicographic path order with
empty precedence,
rule 7
is weakly decreasing and
rule 6
is strictly decreasing.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006