Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
not(and(x,y)) |
→ or(not(x),not(y)) |
| 2: |
|
not(or(x,y)) |
→ and(not(x),not(y)) |
| 3: |
|
and(x,or(y,z)) |
→ or(and(x,y),and(x,z)) |
|
There are 7 dependency pairs:
|
| 4: |
|
NOT(and(x,y)) |
→ NOT(x) |
| 5: |
|
NOT(and(x,y)) |
→ NOT(y) |
| 6: |
|
NOT(or(x,y)) |
→ AND(not(x),not(y)) |
| 7: |
|
NOT(or(x,y)) |
→ NOT(x) |
| 8: |
|
NOT(or(x,y)) |
→ NOT(y) |
| 9: |
|
AND(x,or(y,z)) |
→ AND(x,y) |
| 10: |
|
AND(x,or(y,z)) |
→ AND(x,z) |
|
The approximated dependency graph contains 2 SCCs:
{9,10}
and {4,5,7,8}.
-
Consider the SCC {9,10}.
There are no usable rules.
By taking the AF π with
π(AND) = 2 together with
the lexicographic path order with
empty precedence,
the rules in {9,10}
are strictly decreasing.
-
Consider the SCC {4,5,7,8}.
There are no usable rules.
By taking the AF π with
π(NOT) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {4,5,7,8}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006