Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(x + 0) |
→ f(x) |
| 2: |
|
x + (y + z) |
→ (x + y) + z |
|
There are 3 dependency pairs:
|
| 3: |
|
F(x + 0) |
→ F(x) |
| 4: |
|
x +# (y + z) |
→ (x + y) +# z |
| 5: |
|
x +# (y + z) |
→ x +# y |
|
The approximated dependency graph contains 2 SCCs:
{4,5}
and {3}.
-
Consider the SCC {4,5}.
The usable rules are {2}.
The constraints could not be solved.
-
Consider the SCC {3}.
There are no usable rules.
By taking the AF π with
π(F) = 1
and π(+) = [1] together with
the lexicographic path order with
empty precedence,
rule 3
is strictly decreasing.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006