Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(a,empty) |
→ g(a,empty) |
| 2: |
|
f(a,cons(x,k)) |
→ f(cons(x,a),k) |
| 3: |
|
g(empty,d) |
→ d |
| 4: |
|
g(cons(x,k),d) |
→ g(k,cons(x,d)) |
|
There are 3 dependency pairs:
|
| 5: |
|
F(a,empty) |
→ G(a,empty) |
| 6: |
|
F(a,cons(x,k)) |
→ F(cons(x,a),k) |
| 7: |
|
G(cons(x,k),d) |
→ G(k,cons(x,d)) |
|
The approximated dependency graph contains 2 SCCs:
{7}
and {6}.
-
Consider the SCC {7}.
There are no usable rules.
By taking the AF π with
π(G) = 1
and π(cons) = [2] together with
the lexicographic path order with
empty precedence,
rule 7
is strictly decreasing.
-
Consider the SCC {6}.
There are no usable rules.
By taking the AF π with
π(F) = 2
and π(cons) = [2] together with
the lexicographic path order with
empty precedence,
rule 6
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006