Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(g(x),s(0)) |
→ f(g(x),g(x)) |
| 2: |
|
g(s(x)) |
→ s(g(x)) |
| 3: |
|
g(0) |
→ 0 |
|
There are 2 dependency pairs:
|
| 4: |
|
F(g(x),s(0)) |
→ F(g(x),g(x)) |
| 5: |
|
G(s(x)) |
→ G(x) |
|
The approximated dependency graph contains 2 SCCs:
{4}
and {5}.
-
Consider the SCC {4}.
The usable rules are {2,3}.
The constraints could not be solved.
-
Consider the SCC {5}.
There are no usable rules.
By taking the AF π with
π(G) = 1 together with
the lexicographic path order with
empty precedence,
rule 5
is strictly decreasing.
Tyrolean Termination Tool (0.02 seconds)
--- May 4, 2006