Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
rev(a) |
→ a |
| 2: |
|
rev(b) |
→ b |
| 3: |
|
rev(x ++ y) |
→ rev(y) ++ rev(x) |
| 4: |
|
rev(x ++ x) |
→ rev(x) |
|
There are 3 dependency pairs:
|
| 5: |
|
REV(x ++ y) |
→ REV(y) |
| 6: |
|
REV(x ++ y) |
→ REV(x) |
| 7: |
|
REV(x ++ x) |
→ REV(x) |
|
The approximated dependency graph contains one SCC:
{5-7}.
-
Consider the SCC {5-7}.
There are no usable rules.
By taking the AF π with
π(REV) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {5-7}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.02 seconds)
--- May 3, 2006