* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
concat(cons(U,V),Y) -> cons(U,concat(V,Y))
concat(leaf(),Y) -> Y
lessleaves(X,leaf()) -> false()
lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))
lessleaves(leaf(),cons(W,Z)) -> true()
- Signature:
{concat/2,lessleaves/2} / {cons/2,false/0,leaf/0,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {concat,lessleaves} and constructors {cons,false,leaf
,true}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
concat_0(2,2) -> 1
concat_1(2,2) -> 3
concat_1(2,2) -> 4
concat_1(2,2) -> 5
concat_1(2,3) -> 3
concat_1(2,3) -> 4
concat_1(2,3) -> 5
concat_2(2,3) -> 4
concat_2(2,3) -> 5
cons_0(2,2) -> 1
cons_0(2,2) -> 2
cons_0(2,2) -> 3
cons_0(2,2) -> 4
cons_0(2,2) -> 5
cons_1(2,3) -> 1
cons_1(2,3) -> 3
cons_1(2,3) -> 4
cons_1(2,3) -> 5
false_0() -> 1
false_0() -> 2
false_0() -> 3
false_0() -> 4
false_0() -> 5
false_1() -> 1
leaf_0() -> 1
leaf_0() -> 2
leaf_0() -> 3
leaf_0() -> 4
leaf_0() -> 5
lessleaves_0(2,2) -> 1
lessleaves_1(3,3) -> 1
lessleaves_2(4,5) -> 1
true_0() -> 1
true_0() -> 2
true_0() -> 3
true_0() -> 4
true_0() -> 5
true_1() -> 1
2 -> 1
2 -> 3
2 -> 4
2 -> 5
3 -> 4
3 -> 5
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
concat(cons(U,V),Y) -> cons(U,concat(V,Y))
concat(leaf(),Y) -> Y
lessleaves(X,leaf()) -> false()
lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))
lessleaves(leaf(),cons(W,Z)) -> true()
- Signature:
{concat/2,lessleaves/2} / {cons/2,false/0,leaf/0,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {concat,lessleaves} and constructors {cons,false,leaf
,true}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))