interpretations
Execution Time (secs) | - |
Answer | YES(?,O(n^3)) |
Input | SK90 4.30 |
YES(?,O(n^3))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).
Strict Trs:
{ f(nil()) -> nil()
, f(.(nil(), y)) -> .(nil(), f(y))
, f(.(.(x, y), z)) -> f(.(x, .(y, z)))
, g(nil()) -> nil()
, g(.(x, nil())) -> .(g(x), nil())
, g(.(x, .(y, z))) -> g(.(.(x, y), z)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(f) = {}, Uargs(.) = {1, 2}, Uargs(g) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[1 2 0] [2]
[f](x1) = [1 0 0] x1 + [3]
[2 3 0] [0]
[0]
[nil] = [0]
[0]
[1 3 0] [1 0 0] [1]
[.](x1, x2) = [0 0 0] x1 + [0 1 0] x2 + [1]
[0 1 1] [1 1 0] [0]
[1 1 3] [3]
[g](x1) = [0 1 0] x1 + [0]
[1 1 3] [1]
This order satisfies following ordering constraints
[f(nil())] = [2]
[3]
[0]
> [0]
[0]
[0]
= [nil()]
[f(.(nil(), y))] = [1 2 0] [5]
[1 0 0] y + [4]
[2 3 0] [5]
> [1 2 0] [3]
[1 0 0] y + [4]
[2 2 0] [5]
= [.(nil(), f(y))]
[f(.(.(x, y), z))] = [1 3 0] [1 3 0] [1 2 0] [9]
[1 3 0] y + [1 3 0] x + [1 0 0] z + [8]
[2 6 0] [2 6 0] [2 3 0] [13]
> [1 3 0] [1 3 0] [1 2 0] [8]
[1 3 0] y + [1 3 0] x + [1 0 0] z + [5]
[2 6 0] [2 6 0] [2 3 0] [10]
= [f(.(x, .(y, z)))]
[g(nil())] = [3]
[0]
[1]
> [0]
[0]
[0]
= [nil()]
[g(.(x, nil()))] = [1 6 3] [5]
[0 0 0] x + [1]
[1 6 3] [3]
> [1 4 3] [4]
[0 0 0] x + [1]
[1 2 3] [1]
= [.(g(x), nil())]
[g(.(x, .(y, z)))] = [4 12 0] [1 6 3] [4 4 0] [13]
[0 0 0] y + [0 0 0] x + [0 1 0] z + [2]
[4 12 0] [1 6 3] [4 4 0] [11]
> [4 9 0] [1 6 3] [4 4 0] [12]
[0 0 0] y + [0 0 0] x + [0 1 0] z + [1]
[4 9 0] [1 6 3] [4 4 0] [10]
= [g(.(.(x, y), z))]
Hurray, we answered YES(?,O(n^3))
lmpo
Execution Time (secs) | - |
Answer | MAYBE |
Input | SK90 4.30 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(nil()) -> nil()
, f(.(nil(), y)) -> .(nil(), f(y))
, f(.(.(x, y), z)) -> f(.(x, .(y, z)))
, g(nil()) -> nil()
, g(.(x, nil())) -> .(g(x), nil())
, g(.(x, .(y, z))) -> g(.(.(x, y), z)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
mpo
Execution Time (secs) | - |
Answer | MAYBE |
Input | SK90 4.30 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(nil()) -> nil()
, f(.(nil(), y)) -> .(nil(), f(y))
, f(.(.(x, y), z)) -> f(.(x, .(y, z)))
, g(nil()) -> nil()
, g(.(x, nil())) -> .(g(x), nil())
, g(.(x, .(y, z))) -> g(.(.(x, y), z)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar
Execution Time (secs) | 0.272 |
Answer | MAYBE |
Input | SK90 4.30 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(nil()) -> nil()
, f(.(nil(), y)) -> .(nil(), f(y))
, f(.(.(x, y), z)) -> f(.(x, .(y, z)))
, g(nil()) -> nil()
, g(.(x, nil())) -> .(g(x), nil())
, g(.(x, .(y, z))) -> g(.(.(x, y), z)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar-ps
Execution Time (secs) | 0.345 |
Answer | MAYBE |
Input | SK90 4.30 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(nil()) -> nil()
, f(.(nil(), y)) -> .(nil(), f(y))
, f(.(.(x, y), z)) -> f(.(x, .(y, z)))
, g(nil()) -> nil()
, g(.(x, nil())) -> .(g(x), nil())
, g(.(x, .(y, z))) -> g(.(.(x, y), z)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..