(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:
Knuth-Bendix order [KBO] with precedence:
lessleaves2 > true > false > concat2 > cons2 > leaf
and weight map:
leaf=1
false=2
true=4
concat_2=0
cons_2=1
lessleaves_2=0
The variable weight is 1With 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
lessleaves(cons(U, V), cons(W, Z)) → lessleaves(concat(U, V), concat(W, Z))
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) YES