Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(s(X)) |
→ f(X) |
| 2: |
|
g(cons(0,Y)) |
→ g(Y) |
| 3: |
|
g(cons(s(X),Y)) |
→ s(X) |
| 4: |
|
h(cons(X,Y)) |
→ h(g(cons(X,Y))) |
|
There are 4 dependency pairs:
|
| 5: |
|
F(s(X)) |
→ F(X) |
| 6: |
|
G(cons(0,Y)) |
→ G(Y) |
| 7: |
|
H(cons(X,Y)) |
→ H(g(cons(X,Y))) |
| 8: |
|
H(cons(X,Y)) |
→ G(cons(X,Y)) |
|
The approximated dependency graph contains 2 SCCs:
{5}
and {6}.
-
Consider the SCC {5}.
There are no usable rules.
By taking the AF π with
π(F) = 1 together with
the lexicographic path order with
empty precedence,
rule 5
is strictly decreasing.
-
Consider the SCC {6}.
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 6
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006