Term Rewriting System R:
[x, y, z]
.(.(x, y), z) -> .(x, .(y, z))
Termination of R to be shown.
R
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
.(.(x, y), z) -> .(x, .(y, z))
where the Polynomial interpretation:
| POL(.(x1, x2)) | = 1 + 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