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