Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
i(x) * x |
→ 1 |
| 2: |
|
1 * y |
→ y |
| 3: |
|
x * 0 |
→ 0 |
| 4: |
|
(x * y) * z |
→ x * (y * z) |
|
There are 2 dependency pairs:
|
| 5: |
|
(x * y) *# z |
→ x *# (y * z) |
| 6: |
|
(x * y) *# z |
→ y *# z |
|
Consider the SCC {5,6}.
By taking the AF π with
π(*#) = π(i) = 1 together with
the lexicographic path order with
precedence * ≻ 1,
the rules in {1-6}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006