(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following 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))

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:
[concat2, cons2]
lessleaves2 > false
lessleaves2 > true

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

concat(leaf, Y) → Y
concat(cons(U, V), Y) → cons(U, concat(V, Y))
lessleaves(X, leaf) → false
lessleaves(leaf, cons(W, Z)) → true


(2) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

lessleaves(cons(U, V), cons(W, Z)) → lessleaves(concat(U, V), concat(W, Z))

Q is empty.

(3) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:
lessleaves2 > concat2
cons2 > concat2

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

lessleaves(cons(U, V), cons(W, Z)) → lessleaves(concat(U, V), concat(W, Z))


(4) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(5) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(6) TRUE