Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(0) |
→ s(0) |
| 2: |
|
f(s(0)) |
→ s(s(0)) |
| 3: |
|
f(s(0)) |
→ s(s(0)) * f(0) |
| 4: |
|
f(x + s(0)) |
→ s(s(0)) + f(x) |
| 5: |
|
f(x + y) |
→ f(x) * f(y) |
|
There are 4 dependency pairs:
|
| 6: |
|
F(s(0)) |
→ F(0) |
| 7: |
|
F(x + s(0)) |
→ F(x) |
| 8: |
|
F(x + y) |
→ F(x) |
| 9: |
|
F(x + y) |
→ F(y) |
|
The approximated dependency graph contains one SCC:
{7-9}.
-
Consider the SCC {7-9}.
There are no usable rules.
By taking the AF π with
π(F) = π(s) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {7-9}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.00 seconds)
--- May 4, 2006