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