Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(X) |
→ g(n__h(n__f(X))) |
| 2: |
|
h(X) |
→ n__h(X) |
| 3: |
|
f(X) |
→ n__f(X) |
| 4: |
|
activate(n__h(X)) |
→ h(activate(X)) |
| 5: |
|
activate(n__f(X)) |
→ f(activate(X)) |
| 6: |
|
activate(X) |
→ X |
|
There are 4 dependency pairs:
|
| 7: |
|
ACTIVATE(n__h(X)) |
→ H(activate(X)) |
| 8: |
|
ACTIVATE(n__h(X)) |
→ ACTIVATE(X) |
| 9: |
|
ACTIVATE(n__f(X)) |
→ F(activate(X)) |
| 10: |
|
ACTIVATE(n__f(X)) |
→ ACTIVATE(X) |
|
The approximated dependency graph contains one SCC:
{8,10}.
-
Consider the SCC {8,10}.
There are no usable rules.
By taking the AF π with
π(ACTIVATE) = π(n__f) = 1 together with
the lexicographic path order with
empty precedence,
rule 10
is weakly decreasing and
rule 8
is strictly decreasing.
There is one new SCC.
-
Consider the SCC {10}.
By taking the AF π with
π(ACTIVATE) = 1 together with
the lexicographic path order with
empty precedence,
rule 10
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006