Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(f(x,y,z),u,f(x,y,v)) |
→ f(x,y,f(z,u,v)) |
| 2: |
|
f(x,y,y) |
→ y |
| 3: |
|
f(x,y,g(y)) |
→ x |
| 4: |
|
f(x,x,y) |
→ x |
| 5: |
|
f(g(x),x,y) |
→ y |
|
There are 2 dependency pairs:
|
| 6: |
|
F(f(x,y,z),u,f(x,y,v)) |
→ F(x,y,f(z,u,v)) |
| 7: |
|
F(f(x,y,z),u,f(x,y,v)) |
→ F(z,u,v) |
|
Consider the SCC {6,7}.
By taking the AF π with
π(F) = π(g) = 1
and π(f) = [1, 3] together with
the lexicographic path order with
empty precedence,
the rules in {1-7}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006