Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
0 + y |
→ y |
| 2: |
|
s(x) + y |
→ s(x + y) |
| 3: |
|
s(x) + y |
→ x + s(y) |
|
There are 2 dependency pairs:
|
| 4: |
|
s(x) +# y |
→ x +# y |
| 5: |
|
s(x) +# y |
→ x +# s(y) |
|
The approximated dependency graph contains one SCC:
{4,5}.
-
Consider the SCC {4,5}.
There are no usable rules.
By taking the AF π with
π(+#) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {4,5}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006