interpretations
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ a__f(X1, X2, X3) -> f(X1, X2, X3)
, a__f(a(), X, X) -> a__f(X, a__b(), b())
, a__b() -> a()
, a__b() -> b()
, mark(a()) -> a()
, mark(b()) -> a__b()
, mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(a__f) = {2}, Uargs(mark) = {}, Uargs(f) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[a__f](x1, x2, x3) = [3] x1 + [1] x2 + [2] x3 + [2]
[a] = [1]
[a__b] = [2]
[b] = [0]
[mark](x1) = [3] x1 + [3]
[f](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1]
This order satisfies following ordering constraints
[a__f(X1, X2, X3)] = [3] X1 + [1] X2 + [2] X3 + [2]
> [1] X1 + [1] X2 + [1] X3 + [1]
= [f(X1, X2, X3)]
[a__f(a(), X, X)] = [3] X + [5]
> [3] X + [4]
= [a__f(X, a__b(), b())]
[a__b()] = [2]
> [1]
= [a()]
[a__b()] = [2]
> [0]
= [b()]
[mark(a())] = [6]
> [1]
= [a()]
[mark(b())] = [3]
> [2]
= [a__b()]
[mark(f(X1, X2, X3))] = [3] X1 + [3] X2 + [3] X3 + [6]
> [3] X1 + [3] X2 + [2] X3 + [5]
= [a__f(X1, mark(X2), X3)]
Hurray, we answered YES(?,O(n^1))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ a__f(a(), X, X) -> a__f(X, a__b(), b())
, a__b() -> a()
, mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
, mark(b()) -> a__b()
, mark(a()) -> a()
, a__f(X1, X2, X3) -> f(X1, X2, X3)
, a__b() -> b() }
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:
{ a__f(a(), X, X) -> a__f(X, a__b(), b())
, a__b() -> a()
, mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
, mark(b()) -> a__b()
, mark(a()) -> a()
, a__f(X1, X2, X3) -> f(X1, X2, X3)
, a__b() -> b() }
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:
{ a__f(a(), X, X) -> a__f(X, a__b(), b())
, a__b() -> a()
, mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
, mark(b()) -> a__b()
, mark(a()) -> a()
, a__f(X1, X2, X3) -> f(X1, X2, X3)
, a__b() -> b() }
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:
{ a__f(a(), X, X) -> a__f(X, a__b(), b())
, a__b() -> a()
, mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
, mark(b()) -> a__b()
, mark(a()) -> a()
, a__f(X1, X2, X3) -> f(X1, X2, X3)
, a__b() -> b() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..