interpretations
YES(?,O(n^3))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).
Strict Trs:
{ f(X) -> n__f(X)
, f(n__f(n__a())) -> f(n__g(f(n__a())))
, a() -> n__a()
, g(X) -> n__g(X)
, activate(X) -> X
, activate(n__f(X)) -> f(X)
, activate(n__a()) -> a()
, activate(n__g(X)) -> g(X) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(f) = {1}, Uargs(n__f) = {}, Uargs(n__g) = {1}, Uargs(g) = {},
Uargs(activate) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[3 1 0] [1]
[f](x1) = [0 1 1] x1 + [3]
[0 1 1] [1]
[1 1 0] [0]
[n__f](x1) = [0 0 1] x1 + [3]
[0 1 0] [0]
[0]
[n__a] = [2]
[3]
[1 0 0] [0]
[n__g](x1) = [0 0 0] x1 + [2]
[0 0 0] [0]
[1]
[a] = [2]
[3]
[1 0 0] [3]
[g](x1) = [0 0 0] x1 + [2]
[0 0 0] [0]
[3 3 1] [2]
[activate](x1) = [0 2 1] x1 + [2]
[0 1 1] [0]
This order satisfies following ordering constraints
[f(X)] = [3 1 0] [1]
[0 1 1] X + [3]
[0 1 1] [1]
> [1 1 0] [0]
[0 0 1] X + [3]
[0 1 0] [0]
= [n__f(X)]
[f(n__f(n__a()))] = [13]
[11]
[9]
> [12]
[5]
[3]
= [f(n__g(f(n__a())))]
[a()] = [1]
[2]
[3]
> [0]
[2]
[3]
= [n__a()]
[g(X)] = [1 0 0] [3]
[0 0 0] X + [2]
[0 0 0] [0]
> [1 0 0] [0]
[0 0 0] X + [2]
[0 0 0] [0]
= [n__g(X)]
[activate(X)] = [3 3 1] [2]
[0 2 1] X + [2]
[0 1 1] [0]
> [1 0 0] [0]
[0 1 0] X + [0]
[0 0 1] [0]
= [X]
[activate(n__f(X))] = [3 4 3] [11]
[0 1 2] X + [8]
[0 1 1] [3]
> [3 1 0] [1]
[0 1 1] X + [3]
[0 1 1] [1]
= [f(X)]
[activate(n__a())] = [11]
[9]
[5]
> [1]
[2]
[3]
= [a()]
[activate(n__g(X))] = [3 0 0] [8]
[0 0 0] X + [6]
[0 0 0] [2]
> [1 0 0] [3]
[0 0 0] X + [2]
[0 0 0] [0]
= [g(X)]
Hurray, we answered YES(?,O(n^3))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(n__f(n__a())) -> f(n__g(f(n__a())))
, f(X) -> n__f(X)
, a() -> n__a()
, g(X) -> n__g(X)
, activate(n__f(X)) -> f(X)
, activate(n__a()) -> a()
, activate(n__g(X)) -> g(X)
, activate(X) -> X }
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:
{ f(n__f(n__a())) -> f(n__g(f(n__a())))
, f(X) -> n__f(X)
, a() -> n__a()
, g(X) -> n__g(X)
, activate(n__f(X)) -> f(X)
, activate(n__a()) -> a()
, activate(n__g(X)) -> g(X)
, activate(X) -> X }
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:
{ f(n__f(n__a())) -> f(n__g(f(n__a())))
, f(X) -> n__f(X)
, a() -> n__a()
, g(X) -> n__g(X)
, activate(n__f(X)) -> f(X)
, activate(n__a()) -> a()
, activate(n__g(X)) -> g(X)
, activate(X) -> X }
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:
{ f(n__f(n__a())) -> f(n__g(f(n__a())))
, f(X) -> n__f(X)
, a() -> n__a()
, g(X) -> n__g(X)
, activate(n__f(X)) -> f(X)
, activate(n__a()) -> a()
, activate(n__g(X)) -> g(X)
, activate(X) -> X }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..