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