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))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

CONCAT(cons(U, V), Y) -> CONCAT(V, Y)
LESSLEAVES(cons(U, V), cons(W, Z)) -> LESSLEAVES(concat(U, V), concat(W, Z))
LESSLEAVES(cons(U, V), cons(W, Z)) -> CONCAT(U, V)
LESSLEAVES(cons(U, V), cons(W, Z)) -> CONCAT(W, Z)

Furthermore, R contains two SCCs.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Argument Filtering and Ordering`
`       →DP Problem 2`
`         ↳Remaining`

Dependency Pair:

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

Rules:

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))

The following dependency pair can be strictly oriented:

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

The following rules can be oriented:

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))

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
{concat, cons, true} > false
lessleaves > false
CONCAT > false
leaf > false

resulting in one new DP problem.
Used Argument Filtering System:
CONCAT(x1, x2) -> CONCAT(x1, x2)
cons(x1, x2) -> cons(x1, x2)
concat(x1, x2) -> concat(x1, x2)
lessleaves(x1, x2) -> lessleaves(x1, x2)

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳AFS`
`           →DP Problem 3`
`             ↳Dependency Graph`
`       →DP Problem 2`
`         ↳Remaining`

Dependency Pair:

Rules:

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))

Using the Dependency Graph resulted in no new DP problems.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳AFS`
`       →DP Problem 2`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pair:

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

Rules:

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))

Termination of R could not be shown.
Duration:
0:00 minutes