Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(0) |
→ s(0) |
| 2: |
|
f(s(0)) |
→ s(0) |
| 3: |
|
f(s(s(x))) |
→ f(f(s(x))) |
|
There are 2 dependency pairs:
|
| 4: |
|
F(s(s(x))) |
→ F(f(s(x))) |
| 5: |
|
F(s(s(x))) |
→ F(s(x)) |
|
The approximated dependency graph contains one SCC:
{4,5}.
-
Consider the SCC {4,5}.
By taking the AF π with
π(F) = 1 together with
the lexicographic path order with
precedence s ≈ f,
the rules in {1,3,4}
are weakly decreasing and
the rules in {2,5}
are strictly decreasing.
There is one new SCC.
-
Consider the SCC {4}.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006