Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(f(f(a,b),c),x) |
→ f(b,f(a,f(c,f(b,x)))) |
| 2: |
|
f(x,f(y,z)) |
→ f(f(x,y),z) |
|
There are 6 dependency pairs:
|
| 3: |
|
F(f(f(a,b),c),x) |
→ F(b,f(a,f(c,f(b,x)))) |
| 4: |
|
F(f(f(a,b),c),x) |
→ F(a,f(c,f(b,x))) |
| 5: |
|
F(f(f(a,b),c),x) |
→ F(c,f(b,x)) |
| 6: |
|
F(f(f(a,b),c),x) |
→ F(b,x) |
| 7: |
|
F(x,f(y,z)) |
→ F(f(x,y),z) |
| 8: |
|
F(x,f(y,z)) |
→ F(x,y) |
|
The approximated dependency graph contains one SCC:
{3-8}.
-
Consider the SCC {3-8}.
By taking the AF π with
π(f) = π(F) = 1 together with
the lexicographic path order with
precedence a ≻ b
and a ≻ c,
the rules in {2,4,7,8}
are weakly decreasing and
the rules in {1,3,5,6}
are strictly decreasing.
There is one new SCC.
-
Consider the SCC {4,7,8}.
The constraints could not be solved.
Tyrolean Termination Tool (0.13 seconds)
--- May 4, 2006