interpretations
YES(?,O(n^3))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).
Strict Trs:
{ 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)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(concat) = {}, Uargs(cons) = {2}, Uargs(lessleaves) = {1, 2}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[0 0 2] [1 0 0] [0]
[concat](x1, x2) = [0 0 1] x1 + [0 1 0] x2 + [3]
[0 0 1] [0 2 3] [3]
[0]
[leaf] = [0]
[2]
[0 0 2] [1 0 0] [3]
[cons](x1, x2) = [0 0 1] x1 + [0 1 0] x2 + [1]
[0 0 1] [0 0 1] [2]
[2 2 0] [1 1 0] [1]
[lessleaves](x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0]
[false] = [0]
[0]
[0]
[true] = [0]
[0]
This order satisfies following ordering constraints
[concat(leaf(), Y)] = [1 0 0] [4]
[0 1 0] Y + [5]
[0 2 3] [5]
> [1 0 0] [0]
[0 1 0] Y + [0]
[0 0 1] [0]
= [Y]
[concat(cons(U, V), Y)] = [1 0 0] [0 0 2] [0 0 2] [4]
[0 1 0] Y + [0 0 1] U + [0 0 1] V + [5]
[0 2 3] [0 0 1] [0 0 1] [5]
> [1 0 0] [0 0 2] [0 0 2] [3]
[0 1 0] Y + [0 0 1] U + [0 0 1] V + [4]
[0 2 3] [0 0 1] [0 0 1] [5]
= [cons(U, concat(V, Y))]
[lessleaves(X, leaf())] = [2 2 0] [1]
[0 0 0] X + [0]
[0 0 0] [0]
> [0]
[0]
[0]
= [false()]
[lessleaves(leaf(), cons(W, Z))] = [0 0 3] [1 1 0] [5]
[0 0 0] W + [0 0 0] Z + [0]
[0 0 0] [0 0 0] [0]
> [0]
[0]
[0]
= [true()]
[lessleaves(cons(U, V), cons(W, Z))] = [0 0 6] [2 2 0] [0 0 3] [1 1 0] [13]
[0 0 0] U + [0 0 0] V + [0 0 0] W + [0 0 0] Z + [0]
[0 0 0] [0 0 0] [0 0 0] [0 0 0] [0]
> [0 0 6] [2 2 0] [0 0 3] [1 1 0] [10]
[0 0 0] U + [0 0 0] V + [0 0 0] W + [0 0 0] Z + [0]
[0 0 0] [0 0 0] [0 0 0] [0 0 0] [0]
= [lessleaves(concat(U, V), concat(W, Z))]
Hurray, we answered YES(?,O(n^3))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 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)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
mpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 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)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 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)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar-ps
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ 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)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..