Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(0) |
→ cons(0,n__f(s(0))) |
| 2: |
|
f(s(0)) |
→ f(p(s(0))) |
| 3: |
|
p(s(0)) |
→ 0 |
| 4: |
|
f(X) |
→ n__f(X) |
| 5: |
|
activate(n__f(X)) |
→ f(X) |
| 6: |
|
activate(X) |
→ X |
|
There are 3 dependency pairs:
|
| 7: |
|
F(s(0)) |
→ F(p(s(0))) |
| 8: |
|
F(s(0)) |
→ P(s(0)) |
| 9: |
|
ACTIVATE(n__f(X)) |
→ F(X) |
|
The approximated dependency graph contains one SCC:
{7}.
-
Consider the SCC {7}.
The usable rules are {3}.
By taking the AF π with
π(F) = 1
and π(p) = π(s) = [ ] together with
the lexicographic path order with
precedence s ≻ p ≻ 0,
the rules in {3,7}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006