Termination Proof Script
Consider the TRS R consisting of the rewrite rule
|
| 1: |
|
app(app(apply,f),x) |
→ app(f,x) |
|
There is one dependency pair:
|
| 2: |
|
APP(app(apply,f),x) |
→ APP(f,x) |
|
The approximated dependency graph contains one SCC:
{2}.
-
Consider the SCC {2}.
There are no usable rules.
By taking the AF π with
π(APP) = 1
and π(app) = [2] together with
the lexicographic path order with
empty precedence,
rule 2
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.00 seconds)
--- May 4, 2006