Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(empty,l) |
→ l |
| 2: |
|
f(cons(x,k),l) |
→ g(k,l,cons(x,k)) |
| 3: |
|
g(a,b,c) |
→ f(a,cons(b,c)) |
|
There are 2 dependency pairs:
|
| 4: |
|
F(cons(x,k),l) |
→ G(k,l,cons(x,k)) |
| 5: |
|
G(a,b,c) |
→ F(a,cons(b,c)) |
|
The approximated dependency graph contains one SCC:
{4,5}.
-
Consider the SCC {4,5}.
There are no usable rules.
By taking the AF π with
π(F) = π(G) = 1
and π(cons) = [2] together with
the lexicographic path order with
empty precedence,
rule 5
is weakly decreasing and
rule 4
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.02 seconds)
--- May 3, 2006