Termination Proof Script
Consider the TRS R consisting of the rewrite rule
|
| 1: |
|
f(g(X),Y) |
→ f(X,f(g(X),Y)) |
|
There are 2 dependency pairs:
|
| 2: |
|
F(g(X),Y) |
→ F(X,f(g(X),Y)) |
| 3: |
|
F(g(X),Y) |
→ F(g(X),Y) |
|
The approximated dependency graph contains one SCC:
{2,3}.
-
Consider the SCC {2,3}.
By taking the AF π with
π(f) = π(F) = 1 together with
the lexicographic path order with
empty precedence,
rule 3
is weakly decreasing and
the rules in {1,2}
are strictly decreasing.
There is one new SCC.
-
Consider the SCC {3}.
There are no usable rules.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006