Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
half(0) |
→ 0 |
| 2: |
|
half(s(0)) |
→ 0 |
| 3: |
|
half(s(s(x))) |
→ s(half(x)) |
| 4: |
|
s(log(0)) |
→ s(0) |
| 5: |
|
log(s(x)) |
→ s(log(half(s(x)))) |
|
There are 6 dependency pairs:
|
| 6: |
|
HALF(s(s(x))) |
→ S(half(x)) |
| 7: |
|
HALF(s(s(x))) |
→ HALF(x) |
| 8: |
|
S(log(0)) |
→ S(0) |
| 9: |
|
LOG(s(x)) |
→ S(log(half(s(x)))) |
| 10: |
|
LOG(s(x)) |
→ LOG(half(s(x))) |
| 11: |
|
LOG(s(x)) |
→ HALF(s(x)) |
|
The approximated dependency graph contains 2 SCCs:
{7}
and {10}.
-
Consider the SCC {7}.
There are no usable rules.
By taking the AF π with
π(HALF) = 1 together with
the lexicographic path order with
empty precedence,
rule 7
is strictly decreasing.
-
Consider the SCC {10}.
The usable rules are {1-4}.
The constraints could not be solved.
Tyrolean Termination Tool (0.02 seconds)
--- May 3, 2006