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