Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
(x - y) + z |
→ (x + z) - y |
| 2: |
|
(x + y) - y |
→ x |
|
There are 2 dependency pairs:
|
| 3: |
|
(x - y) +# z |
→ (x + z) -# y |
| 4: |
|
(x - y) +# z |
→ x +# z |
|
The approximated dependency graph contains one SCC:
{4}.
-
Consider the SCC {4}.
There are no usable rules.
By taking the AF π with
π(+#) = 1
and π(-) = [1] together with
the lexicographic path order with
empty precedence,
rule 4
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006