Term Rewriting System R:
[x, y]
or(x, x) -> x
and(x, x) -> x
not(not(x)) -> x
not(and(x, y)) -> or(not(x), not(y))
not(or(x, y)) -> and(not(x), not(y))
Termination of R to be shown.
R
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
or(x, x) -> x
and(x, x) -> x
where the Polynomial interpretation:
| POL(and(x1, x2)) | = 1 + x1 + x2 |
| POL(or(x1, x2)) | = 1 + x1 + x2 |
| POL(not(x1)) | = x1 |
was used.
Not all Rules of R can be deleted, so we still have to regard a part of R.
R
↳RRRPolo
→TRS2
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
not(and(x, y)) -> or(not(x), not(y))
not(or(x, y)) -> and(not(x), not(y))
where the Polynomial interpretation:
| POL(and(x1, x2)) | = 1 + x1 + x2 |
| POL(or(x1, x2)) | = 1 + x1 + x2 |
| POL(not(x1)) | = 2·x1 |
was used.
Not all Rules of R can be deleted, so we still have to regard a part of R.
R
↳RRRPolo
→TRS2
↳RRRPolo
→TRS3
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
not(not(x)) -> x
where the Polynomial interpretation:
was used.
All Rules of R can be deleted.
R
↳RRRPolo
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS4
↳Overlay and local confluence Check
The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost.
R
↳RRRPolo
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS5
↳Dependency Pair Analysis
R contains no Dependency Pairs and therefore no SCCs.
Termination of R successfully shown.
Duration:
0:00 minutes