Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
and(true,X) |
→ X |
| 2: |
|
and(false,Y) |
→ false |
| 3: |
|
if(true,X,Y) |
→ X |
| 4: |
|
if(false,X,Y) |
→ Y |
| 5: |
|
add(0,X) |
→ X |
| 6: |
|
add(s(X),Y) |
→ s(add(X,Y)) |
| 7: |
|
first(0,X) |
→ nil |
| 8: |
|
first(s(X),cons(Y,Z)) |
→ cons(Y,first(X,Z)) |
| 9: |
|
from(X) |
→ cons(X,from(s(X))) |
|
There are 3 dependency pairs:
|
| 10: |
|
ADD(s(X),Y) |
→ ADD(X,Y) |
| 11: |
|
FIRST(s(X),cons(Y,Z)) |
→ FIRST(X,Z) |
| 12: |
|
FROM(X) |
→ FROM(s(X)) |
|
The approximated dependency graph contains 3 SCCs:
{10},
{11}
and {12}.
-
Consider the SCC {10}.
There are no usable rules.
By taking the AF π with
π(ADD) = 1 together with
the lexicographic path order with
empty precedence,
rule 10
is strictly decreasing.
-
Consider the SCC {11}.
There are no usable rules.
By taking the AF π with
π(FIRST) = 1 together with
the lexicographic path order with
empty precedence,
rule 11
is strictly decreasing.
-
Consider the SCC {12}.
There are no usable rules.
The constraints could not be solved.
Tyrolean Termination Tool (0.02 seconds)
--- May 4, 2006