Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
app(f,app(g,x)) |
→ app(g,app(g,app(f,x))) |
| 2: |
|
app(f,app(g,x)) |
→ app(g,app(g,app(g,x))) |
|
There are 5 dependency pairs:
|
| 3: |
|
APP(f,app(g,x)) |
→ APP(g,app(g,app(f,x))) |
| 4: |
|
APP(f,app(g,x)) |
→ APP(g,app(f,x)) |
| 5: |
|
APP(f,app(g,x)) |
→ APP(f,x) |
| 6: |
|
APP(f,app(g,x)) |
→ APP(g,app(g,app(g,x))) |
| 7: |
|
APP(f,app(g,x)) |
→ APP(g,app(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(APP) = 2
and π(app) = [2] 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