Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
app(f,app(f,x)) |
→ app(g,app(f,x)) |
| 2: |
|
app(g,app(g,x)) |
→ app(f,x) |
|
There are 2 dependency pairs:
|
| 3: |
|
APP(f,app(f,x)) |
→ APP(g,app(f,x)) |
| 4: |
|
APP(g,app(g,x)) |
→ APP(f,x) |
|
Consider the SCC {3,4}.
By taking the AF π with
π(APP) = 2
and π(app) = [2] together with
the lexicographic path order with
empty precedence,
the rules in {1,3}
are weakly decreasing and
the rules in {2,4}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.02 seconds)
--- May 4, 2006