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(n__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(activate(X)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(f) = {}, Uargs(n__f) = {}, Uargs(n__g) = {}, Uargs(g) = {1},
Uargs(activate) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[0 3 0] [1]
[f](x1) = [0 1 0] x1 + [0]
[0 0 0] [0]
[0 2 0] [0]
[n__f](x1) = [0 1 0] x1 + [0]
[0 0 0] [0]
[0]
[n__a] = [1]
[0]
[1 3 1] [0]
[n__g](x1) = [0 0 1] x1 + [0]
[0 1 0] [1]
[1]
[a] = [1]
[0]
[1 3 1] [1]
[g](x1) = [0 0 1] x1 + [0]
[0 1 0] [1]
[1 3 3] [2]
[activate](x1) = [0 1 0] x1 + [0]
[0 0 1] [0]
This order satisfies following ordering constraints
[f(X)] = [0 3 0] [1]
[0 1 0] X + [0]
[0 0 0] [0]
> [0 2 0] [0]
[0 1 0] X + [0]
[0 0 0] [0]
= [n__f(X)]
[f(n__f(n__a()))] = [4]
[1]
[0]
> [1]
[0]
[0]
= [f(n__g(n__f(n__a())))]
[a()] = [1]
[1]
[0]
> [0]
[1]
[0]
= [n__a()]
[g(X)] = [1 3 1] [1]
[0 0 1] X + [0]
[0 1 0] [1]
> [1 3 1] [0]
[0 0 1] X + [0]
[0 1 0] [1]
= [n__g(X)]
[activate(X)] = [1 3 3] [2]
[0 1 0] X + [0]
[0 0 1] [0]
> [1 0 0] [0]
[0 1 0] X + [0]
[0 0 1] [0]
= [X]
[activate(n__f(X))] = [0 5 0] [2]
[0 1 0] X + [0]
[0 0 0] [0]
> [0 3 0] [1]
[0 1 0] X + [0]
[0 0 0] [0]
= [f(X)]
[activate(n__a())] = [5]
[1]
[0]
> [1]
[1]
[0]
= [a()]
[activate(n__g(X))] = [1 6 4] [5]
[0 0 1] X + [0]
[0 1 0] [1]
> [1 6 4] [3]
[0 0 1] X + [0]
[0 1 0] [1]
= [g(activate(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(n__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(activate(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(n__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(activate(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(n__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(activate(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(n__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(activate(X))
, activate(X) -> X }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..