Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
from(X) |
→ cons(X,from(s(X))) |
| 2: |
|
first(0,Z) |
→ nil |
| 3: |
|
first(s(X),cons(Y,Z)) |
→ cons(Y,first(X,Z)) |
| 4: |
|
sel(0,cons(X,Z)) |
→ X |
| 5: |
|
sel(s(X),cons(Y,Z)) |
→ sel(X,Z) |
|
There are 3 dependency pairs:
|
| 6: |
|
FROM(X) |
→ FROM(s(X)) |
| 7: |
|
FIRST(s(X),cons(Y,Z)) |
→ FIRST(X,Z) |
| 8: |
|
SEL(s(X),cons(Y,Z)) |
→ SEL(X,Z) |
|
The approximated dependency graph contains 3 SCCs:
{7},
{6}
and {8}.
-
Consider the SCC {7}.
There are no usable rules.
By taking the AF π with
π(FIRST) = 1 together with
the lexicographic path order with
empty precedence,
rule 7
is strictly decreasing.
-
Consider the SCC {6}.
There are no usable rules.
The constraints could not be solved.
-
Consider the SCC {8}.
There are no usable rules.
By taking the AF π with
π(SEL) = 1 together with
the lexicographic path order with
empty precedence,
rule 8
is strictly decreasing.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006