Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
merge(x,nil) |
→ x |
| 2: |
|
merge(nil,y) |
→ y |
| 3: |
|
merge(x ++ y,u ++ v) |
→ x ++ merge(y,u ++ v) |
| 4: |
|
merge(x ++ y,u ++ v) |
→ u ++ merge(x ++ y,v) |
|
There are 2 dependency pairs:
|
| 5: |
|
MERGE(x ++ y,u ++ v) |
→ MERGE(y,u ++ v) |
| 6: |
|
MERGE(x ++ y,u ++ v) |
→ MERGE(x ++ y,v) |
|
The approximated dependency graph contains one SCC:
{5}.
-
Consider the SCC {5}.
There are no usable rules.
By taking the AF π with
π(MERGE) = 1
and π(++) = [2] together with
the lexicographic path order with
empty precedence,
rule 5
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.00 seconds)
--- May 4, 2006