Term Rewriting System R:
[x, y]
f(s(x), y) -> f(x, s(x))
f(x, s(y)) -> f(y, x)
Termination of R to be shown.
R
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
f(s(x), y) -> f(x, s(x))
f(x, s(y)) -> f(y, x)
where the Polynomial interpretation:
| POL(s(x1)) | = 1 + 2·x1 |
| POL(f(x1, x2)) | = 2 + 2·x1 + x2 |
was used.
All Rules of R can be deleted.
R
↳RRRPolo
→TRS2
↳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
↳OC
→TRS3
↳Dependency Pair Analysis
R contains no Dependency Pairs and therefore no SCCs.
Termination of R successfully shown.
Duration:
0:00 minutes