Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(a,f(b,x)) |
→ f(b,f(a,x)) |
| 2: |
|
f(b,f(c,x)) |
→ f(c,f(b,x)) |
| 3: |
|
f(c,f(a,x)) |
→ f(a,f(c,x)) |
|
There are 6 dependency pairs:
|
| 4: |
|
F(a,f(b,x)) |
→ F(b,f(a,x)) |
| 5: |
|
F(a,f(b,x)) |
→ F(a,x) |
| 6: |
|
F(b,f(c,x)) |
→ F(c,f(b,x)) |
| 7: |
|
F(b,f(c,x)) |
→ F(b,x) |
| 8: |
|
F(c,f(a,x)) |
→ F(a,f(c,x)) |
| 9: |
|
F(c,f(a,x)) |
→ F(c,x) |
|
The approximated dependency graph contains one SCC:
{4-9}.
-
Consider the SCC {4-9}.
By taking the AF π with
π(F) = 2
and π(f) = [2] together with
the lexicographic path order with
empty precedence,
the rules in {1-4,6,8}
are weakly decreasing and
the rules in {5,7,9}
are strictly decreasing.
There is one new SCC.
-
Consider the SCC {4,6,8}.
The constraints could not be solved.
Tyrolean Termination Tool (0.99 seconds)
--- May 4, 2006