Term Rewriting System R:
[x]
a(a(x)) -> b(b(x))
b(b(a(x))) -> a(b(b(x)))
Termination of R to be shown.
TRS
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
a(a(x)) -> b(b(x))
where the Polynomial interpretation:
| POL(b(x1)) | = x1 |
| POL(a(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
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
b(b(a(x))) -> a(b(b(x)))
where the Polynomial interpretation:
| POL(b(x1)) | = 2·x1 |
| POL(a(x1)) | = 1 + x1 |
was used.
All Rules of R can be deleted.
TRS
↳RRRPolo
→TRS2
↳RRRPolo
→TRS3
↳Dependency Pair Analysis
R contains no Dependency Pairs and therefore no SCCs.
Termination of R successfully shown.
Duration:
0:01 minutes