Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(0,1,x) |
→ f(g(x),g(x),x) |
| 2: |
|
f(g(x),y,z) |
→ g(f(x,y,z)) |
| 3: |
|
f(x,g(y),z) |
→ g(f(x,y,z)) |
| 4: |
|
f(x,y,g(z)) |
→ g(f(x,y,z)) |
|
There are 4 dependency pairs:
|
| 5: |
|
F(0,1,x) |
→ F(g(x),g(x),x) |
| 6: |
|
F(g(x),y,z) |
→ F(x,y,z) |
| 7: |
|
F(x,g(y),z) |
→ F(x,y,z) |
| 8: |
|
F(x,y,g(z)) |
→ F(x,y,z) |
|
The approximated dependency graph contains one SCC:
{5-8}.
-
Consider the SCC {5-8}.
There are no usable rules.
By taking the AF π with
π(F) = 3 together with
the lexicographic path order with
empty precedence,
the rules in {5-7}
are weakly decreasing and
rule 8
is strictly decreasing.
There is one new SCC.
-
Consider the SCC {5-7}.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006