Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(f(x)) |
→ f(x) |
| 2: |
|
f(s(x)) |
→ f(x) |
| 3: |
|
g(s(0)) |
→ g(f(s(0))) |
|
There are 3 dependency pairs:
|
| 4: |
|
F(s(x)) |
→ F(x) |
| 5: |
|
G(s(0)) |
→ G(f(s(0))) |
| 6: |
|
G(s(0)) |
→ F(s(0)) |
|
The approximated dependency graph contains one SCC:
{4}.
-
Consider the SCC {4}.
There are no usable rules.
By taking the AF π with
π(F) = 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 3, 2006