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