Term Rewriting System R:
[m, n, r]
p(m, n, s(r)) -> p(m, r, n)
p(m, s(n), 0) -> p(0, n, m)
p(m, 0, 0) -> m
Termination of R to be shown.
R
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
p(m, n, s(r)) -> p(m, r, n)
p(m, s(n), 0) -> p(0, n, m)
where the Polynomial interpretation:
| POL(0) | = 0 |
| POL(s(x1)) | = 1 + x1 |
| POL(p(x1, x2, x3)) | = x1 + x2 + x3 |
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:
p(m, 0, 0) -> m
where the Polynomial interpretation:
| POL(0) | = 0 |
| POL(p(x1, x2, x3)) | = 1 + x1 + x2 + x3 |
was used.
All Rules of R can be deleted.
R
↳RRRPolo
→TRS2
↳RRRPolo
→TRS3
↳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
↳OC
...
→TRS4
↳Dependency Pair Analysis
R contains no Dependency Pairs and therefore no SCCs.
Termination of R successfully shown.
Duration:
0:00 minutes