Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
(x * y) + (a * y) |
→ (x + a) * y |
| 2: |
|
(x * y) * z |
→ x * (y * z) |
|
There are 4 dependency pairs:
|
| 3: |
|
(x * y) +# (a * y) |
→ (x + a) *# y |
| 4: |
|
(x * y) +# (a * y) |
→ x +# a |
| 5: |
|
(x * y) *# z |
→ x *# (y * z) |
| 6: |
|
(x * y) *# z |
→ y *# z |
|
The approximated dependency graph contains one SCC:
{5,6}.
-
Consider the SCC {5,6}.
The usable rules are {2}.
By taking the AF π with
π(*#) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {2,5,6}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006