Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(g(a)) |
→ f(s(g(b))) |
| 2: |
|
f(f(x)) |
→ b |
| 3: |
|
g(x) |
→ f(g(x)) |
|
There are 4 dependency pairs:
|
| 4: |
|
F(g(a)) |
→ F(s(g(b))) |
| 5: |
|
F(g(a)) |
→ G(b) |
| 6: |
|
G(x) |
→ F(g(x)) |
| 7: |
|
G(x) |
→ G(x) |
|
The approximated dependency graph contains one SCC:
{5-7}.
-
Consider the SCC {5-7}.
By taking the AF π with
π(F) = 1
and π(f) = [ ] together with
the lexicographic path order with
precedence a ≻ G ≻ g ≻ f ≻ b,
the rules in {1,7}
are weakly decreasing and
the rules in {2,3,5,6}
are strictly decreasing.
There is one new SCC.
-
Consider the SCC {7}.
There are no usable rules.
The constraints could not be solved.
Tyrolean Termination Tool (0.02 seconds)
--- May 3, 2006