Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
x + (y + z) |
→ (x + y) + z |
| 2: |
|
(x * y) + (x + z) |
→ x * (y + z) |
| 3: |
|
(x * y) + ((x * z) + u) |
→ (x * (y + z)) + u |
|
There are 5 dependency pairs:
|
| 4: |
|
x +# (y + z) |
→ (x + y) +# z |
| 5: |
|
x +# (y + z) |
→ x +# y |
| 6: |
|
(x * y) +# (x + z) |
→ y +# z |
| 7: |
|
(x * y) +# ((x * z) + u) |
→ (x * (y + z)) +# u |
| 8: |
|
(x * y) +# ((x * z) + u) |
→ y +# z |
|
The approximated dependency graph contains one SCC:
{4-8}.
-
Consider the SCC {4-8}.
By taking the AF π with
π(+) = π(+#) = 1
and π(*) = [2] together with
the lexicographic path order with
empty precedence,
the rules in {1-5,7}
are weakly decreasing and
the rules in {6,8}
are strictly decreasing.
There is one new SCC.
-
Consider the SCC {4,5,7}.
The constraints could not be solved.
Tyrolean Termination Tool (0.03 seconds)
--- May 3, 2006