interpretations
YES(?,O(n^3))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).
Strict Trs:
{ f(c(s(x), y)) -> f(c(x, s(y)))
, g(c(x, s(y))) -> g(c(s(x), y)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(f) = {}, Uargs(c) = {}, Uargs(s) = {}, Uargs(g) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[1 0 1] [3]
[f](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 2] [0 0 0] [0]
[c](x1, x2) = [0 0 1] x1 + [1 0 2] x2 + [0]
[0 0 0] [0 0 0] [3]
[1 1 3] [1]
[s](x1) = [0 0 3] x1 + [0]
[0 0 1] [3]
[1 2 0] [1]
[g](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
This order satisfies following ordering constraints
[f(c(s(x), y))] = [0 0 2] [12]
[0 0 0] x + [0]
[0 0 0] [0]
> [0 0 2] [6]
[0 0 0] x + [0]
[0 0 0] [0]
= [f(c(x, s(y)))]
[g(c(x, s(y)))] = [0 0 4] [2 2 10] [15]
[0 0 0] x + [0 0 0] y + [0]
[0 0 0] [0 0 0] [0]
> [0 0 4] [2 0 4] [13]
[0 0 0] x + [0 0 0] y + [0]
[0 0 0] [0 0 0] [0]
= [g(c(s(x), y))]
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(c(s(x), y)) -> f(c(x, s(y)))
, g(c(x, s(y))) -> g(c(s(x), y)) }
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(c(s(x), y)) -> f(c(x, s(y)))
, g(c(x, s(y))) -> g(c(s(x), y)) }
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(c(s(x), y)) -> f(c(x, s(y)))
, g(c(x, s(y))) -> g(c(s(x), y)) }
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(c(s(x), y)) -> f(c(x, s(y)))
, g(c(x, s(y))) -> g(c(s(x), y)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..