Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
x * (y + z) |
→ (x * y) + (x * z) |
| 2: |
|
(y + z) * x |
→ (x * y) + (x * z) |
| 3: |
|
(x * y) * z |
→ x * (y * z) |
| 4: |
|
(x + y) + z |
→ x + (y + z) |
|
There are 10 dependency pairs:
|
| 5: |
|
x *# (y + z) |
→ (x * y) +# (x * z) |
| 6: |
|
x *# (y + z) |
→ x *# y |
| 7: |
|
x *# (y + z) |
→ x *# z |
| 8: |
|
(y + z) *# x |
→ (x * y) +# (x * z) |
| 9: |
|
(y + z) *# x |
→ x *# y |
| 10: |
|
(y + z) *# x |
→ x *# z |
| 11: |
|
(x * y) *# z |
→ x *# (y * z) |
| 12: |
|
(x * y) *# z |
→ y *# z |
| 13: |
|
(x + y) +# z |
→ x +# (y + z) |
| 14: |
|
(x + y) +# z |
→ y +# z |
|
The approximated dependency graph contains 2 SCCs:
{13,14}
and {6,7,9-12}.
-
Consider the SCC {13,14}.
The usable rules are {4}.
By taking the AF π with
π(+#) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {4,13,14}
are strictly decreasing.
-
Consider the SCC {6,7,9-12}.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006