Term Rewriting System R:
[X, XS]
zeros -> cons(0, nzeros)
zeros -> nzeros
tail(cons(X, XS)) -> activate(XS)
activate(nzeros) -> zeros
activate(X) -> X

Innermost Termination of R to be shown.

`   R`
`     ↳Removing Redundant Rules`

Removing the following rules from R which fullfill a polynomial ordering:

zeros -> cons(0, nzeros)
zeros -> nzeros
activate(X) -> X

where the Polynomial interpretation:
 POL(activate(x1)) =  1 + x1 POL(n__zeros) =  0 POL(0) =  0 POL(cons(x1, x2)) =  x1 + x2 POL(tail(x1)) =  1 + x1 POL(zeros) =  1
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:

activate(nzeros) -> zeros

where the Polynomial interpretation:
 POL(activate(x1)) =  x1 POL(n__zeros) =  1 POL(cons(x1, x2)) =  x1 + x2 POL(tail(x1)) =  x1 POL(zeros) =  0
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳RRRPolo`
`           →TRS3`
`             ↳Removing Redundant Rules`

Removing the following rules from R which fullfill a polynomial ordering:

tail(cons(X, XS)) -> activate(XS)

where the Polynomial interpretation:
 POL(activate(x1)) =  x1 POL(cons(x1, x2)) =  x1 + x2 POL(tail(x1)) =  1 + x1
was used.

All Rules of R can be deleted.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳RRRPolo`
`           →TRS3`
`             ↳RRRPolo`
`             ...`
`               →TRS4`
`                 ↳Dependency Pair Analysis`

R contains no Dependency Pairs and therefore no SCCs.

Innermost Termination of R successfully shown.
Duration:
0:00 minutes