Term Rewriting System R:
[X, Y, Z]
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
times(X, s(Y)) -> plus(X, times(Y, X))
Termination of R to be shown.
R
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
times(X, s(Y)) -> plus(X, times(Y, X))
where the Polynomial interpretation:
| POL(plus(x1, x2)) | = x1 + x2 |
| POL(times(x1, x2)) | = 2·x1 + x2 |
| POL(s(x1)) | = 1 + 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
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
where the Polynomial interpretation:
| POL(plus(x1, x2)) | = 1 + 2·x1 + x2 |
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