Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
rev(ls) |
→ r1(ls,empty) |
| 2: |
|
r1(empty,a) |
→ a |
| 3: |
|
r1(cons(x,k),a) |
→ r1(k,cons(x,a)) |
|
There are 2 dependency pairs:
|
| 4: |
|
REV(ls) |
→ R1(ls,empty) |
| 5: |
|
R1(cons(x,k),a) |
→ R1(k,cons(x,a)) |
|
The approximated dependency graph contains one SCC:
{5}.
-
Consider the SCC {5}.
There are no usable rules.
By taking the AF π with
π(R1) = 1
and π(cons) = [2] together with
the lexicographic path order with
empty precedence,
rule 5
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006