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