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