Termination Proof Script
Consider the TRS R consisting of the rewrite rule
|
| 1: |
|
f(f(a,f(x,a)),a) |
→ f(a,f(f(x,a),a)) |
|
There are 2 dependency pairs:
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| 2: |
|
F(f(a,f(x,a)),a) |
→ F(a,f(f(x,a),a)) |
| 3: |
|
F(f(a,f(x,a)),a) |
→ F(f(x,a),a) |
|
The approximated dependency graph contains one SCC:
{3}.
-
Consider the SCC {3}.
By taking the AF π with
π(F) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {1,3}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.00 seconds)
--- May 4, 2006