interpretations
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ g(x, s(y)) -> g(f(x, y), 0())
, g(0(), f(x, x)) -> x
, g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
, g(s(x), y) -> g(f(x, y), 0()) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(g) = {}, Uargs(f) = {1, 2}, Uargs(s) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[g](x1, x2) = [3] x1 + [3] x2 + [1]
[0] = [0]
[f](x1, x2) = [1] x1 + [1] x2 + [2]
[s](x1) = [1] x1 + [3]
This order satisfies following ordering constraints
[g(x, s(y))] = [3] x + [3] y + [10]
> [3] x + [3] y + [7]
= [g(f(x, y), 0())]
[g(0(), f(x, x))] = [6] x + [7]
> [1] x + [0]
= [x]
[g(f(x, y), 0())] = [3] x + [3] y + [7]
> [3] x + [3] y + [4]
= [f(g(x, 0()), g(y, 0()))]
[g(s(x), y)] = [3] x + [3] y + [10]
> [3] x + [3] y + [7]
= [g(f(x, y), 0())]
Hurray, we answered YES(?,O(n^1))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ g(0(), f(x, x)) -> x
, g(x, s(y)) -> g(f(x, y), 0())
, g(s(x), y) -> g(f(x, y), 0())
, g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0())) }
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:
{ g(0(), f(x, x)) -> x
, g(x, s(y)) -> g(f(x, y), 0())
, g(s(x), y) -> g(f(x, y), 0())
, g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0())) }
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:
{ g(0(), f(x, x)) -> x
, g(x, s(y)) -> g(f(x, y), 0())
, g(s(x), y) -> g(f(x, y), 0())
, g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0())) }
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:
{ g(0(), f(x, x)) -> x
, g(x, s(y)) -> g(f(x, y), 0())
, g(s(x), y) -> g(f(x, y), 0())
, g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0())) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..