Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(a,g(y)) |
→ g(g(y)) |
| 2: |
|
f(g(x),a) |
→ f(x,g(a)) |
| 3: |
|
f(g(x),g(y)) |
→ h(g(y),x,g(y)) |
| 4: |
|
h(g(x),y,z) |
→ f(y,h(x,y,z)) |
| 5: |
|
h(a,y,z) |
→ z |
|
There are 4 dependency pairs:
|
| 6: |
|
F(g(x),a) |
→ F(x,g(a)) |
| 7: |
|
F(g(x),g(y)) |
→ H(g(y),x,g(y)) |
| 8: |
|
H(g(x),y,z) |
→ F(y,h(x,y,z)) |
| 9: |
|
H(g(x),y,z) |
→ H(x,y,z) |
|
The approximated dependency graph contains one SCC:
{6-9}.
-
Consider the SCC {6-9}.
By taking the AF π with
π(f) = π(F) = 2,
π(h) = π(H) = 3
and π(g) = [ ] together with
the lexicographic path order with
precedence a ≻ g,
the rules in {1,3-5,7-9}
are weakly decreasing and
the rules in {2,6}
are strictly decreasing.
There is one new SCC.
-
Consider the SCC {7-9}.
The constraints could not be solved.
Tyrolean Termination Tool (0.09 seconds)
--- May 4, 2006