Term Rewriting System R:
[YS, X, XS, Y, L]
app(nil, YS) -> YS
app(cons(X), YS) -> cons(X)
from(X) -> cons(X)
prefix(L) -> cons(nil)

Termination of R to be shown.

`   R`
`     ↳Removing Redundant Rules`

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

app(nil, YS) -> YS
app(cons(X), YS) -> cons(X)

where the Polynomial interpretation:
 POL(from(x1)) =  x1 POL(cons(x1)) =  x1 POL(nil) =  0 POL(app(x1, x2)) =  1 + x1 + x2 POL(prefix(x1)) =  x1 POL(zWadr(x1, x2)) =  1 + x1 + x2
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:

prefix(L) -> cons(nil)

where the Polynomial interpretation:
 POL(from(x1)) =  x1 POL(cons(x1)) =  x1 POL(nil) =  0 POL(app(x1, x2)) =  x1 + x2 POL(prefix(x1)) =  1 + x1 POL(zWadr(x1, x2)) =  x1 + x2
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:

from(X) -> cons(X)

where the Polynomial interpretation:
 POL(from(x1)) =  1 + x1 POL(cons(x1)) =  x1 POL(app(x1, x2)) =  x1 + x2 POL(zWadr(x1, x2)) =  x1 + x2
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`
`             ↳RRRPolo`
`             ...`
`               →TRS4`
`                 ↳Removing Redundant Rules`

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

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

All Rules of R can be deleted.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳RRRPolo`
`           →TRS3`
`             ↳RRRPolo`
`             ...`
`               →TRS5`
`                 ↳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`
`         ↳RRRPolo`
`           →TRS3`
`             ↳RRRPolo`
`             ...`
`               →TRS6`
`                 ↳Dependency Pair Analysis`

R contains no Dependency Pairs and therefore no SCCs.

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