Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
g(h(g(x))) |
→ g(x) |
| 2: |
|
g(g(x)) |
→ g(h(g(x))) |
| 3: |
|
h(h(x)) |
→ h(f(h(x),x)) |
|
There are 3 dependency pairs:
|
| 4: |
|
G(g(x)) |
→ G(h(g(x))) |
| 5: |
|
G(g(x)) |
→ H(g(x)) |
| 6: |
|
H(h(x)) |
→ H(f(h(x),x)) |
|
The approximated dependency graph contains one SCC:
{4}.
-
Consider the SCC {4}.
By taking the AF π with
π(G) = 1
and π(g) = π(h) = [ ] together with
the lexicographic path order with
precedence g ≻ h,
the rules in {1-3}
are weakly decreasing and
rule 4
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.00 seconds)
--- May 4, 2006