Term Rewriting System R:
[x]
w(r(x)) -> r(w(x))
b(r(x)) -> r(b(x))
b(w(x)) -> w(b(x))
Termination of R to be shown.
TRS
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
b(w(x)) -> w(b(x))
where the Polynomial interpretation:
| POL(b(x1)) | = 2·x1 |
| POL(w(x1)) | = 1 + x1 |
| POL(r(x1)) | = x1 |
was used.
Not all Rules of R can be deleted, so we still have to regard a part of R.
TRS
↳RRRPolo
→TRS2
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
b(r(x)) -> r(b(x))
where the Polynomial interpretation:
| POL(b(x1)) | = 2·x1 |
| POL(w(x1)) | = x1 |
| POL(r(x1)) | = 1 + x1 |
was used.
Not all Rules of R can be deleted, so we still have to regard a part of R.
TRS
↳RRRPolo
→TRS2
↳RRRPolo
→TRS3
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
w(r(x)) -> r(w(x))
where the Polynomial interpretation:
| POL(w(x1)) | = 2·x1 |
| POL(r(x1)) | = 1 + x1 |
was used.
All Rules of R can be deleted.
TRS
↳RRRPolo
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS4
↳Dependency Pair Analysis
R contains no Dependency Pairs and therefore no SCCs.
Termination of R successfully shown.
Duration:
0:01 minutes