Term Rewriting System R:
[Y, U, V, X, W, Z]
concat(leaf, Y) -> Y
concat(cons(U, V), Y) -> cons(U, concat(V, Y))
lessleaves(X, leaf) -> false
lessleaves(leaf, cons(W, Z)) -> true
lessleaves(cons(U, V), cons(W, Z)) -> lessleaves(concat(U, V), concat(W, Z))

Innermost Termination of R to be shown.

`   R`
`     ↳Removing Redundant Rules`

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

concat(leaf, Y) -> Y
lessleaves(X, leaf) -> false
lessleaves(leaf, cons(W, Z)) -> true

where the Polynomial interpretation:
 POL(cons(x1, x2)) =  x1 + x2 POL(false) =  0 POL(lessleaves(x1, x2)) =  x1 + x2 POL(true) =  0 POL(leaf) =  1 POL(concat(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`
`         ↳Removing Redundant Rules`

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

lessleaves(cons(U, V), cons(W, Z)) -> lessleaves(concat(U, V), concat(W, Z))

where the Polynomial interpretation:
 POL(cons(x1, x2)) =  1 + x1 + x2 POL(lessleaves(x1, x2)) =  x1 + x2 POL(concat(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:

concat(cons(U, V), Y) -> cons(U, concat(V, Y))

where the Polynomial interpretation:
 POL(cons(x1, x2)) =  1 + x1 + x2 POL(concat(x1, x2)) =  2·x1 + x2
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