interpretations
YES(?,O(n^3))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).
Strict Trs:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, bits(0()) -> 0()
, bits(s(x)) -> s(bits(half(s(x)))) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(half) = {}, Uargs(s) = {1}, Uargs(bits) = {1}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[1 0 0] [1]
[half](x1) = [0 0 1] x1 + [0]
[0 0 1] [0]
[2]
[0] = [0]
[0]
[1 0 0] [3]
[s](x1) = [1 0 0] x1 + [2]
[1 0 0] [0]
[2 3 3] [0]
[bits](x1) = [3 3 2] x1 + [0]
[3 3 2] [0]
This order satisfies following ordering constraints
[half(0())] = [3]
[0]
[0]
> [2]
[0]
[0]
= [0()]
[half(s(0()))] = [6]
[2]
[2]
> [2]
[0]
[0]
= [0()]
[half(s(s(x)))] = [1 0 0] [7]
[1 0 0] x + [3]
[1 0 0] [3]
> [1 0 0] [4]
[1 0 0] x + [3]
[1 0 0] [1]
= [s(half(x))]
[bits(0())] = [4]
[6]
[6]
> [2]
[0]
[0]
= [0()]
[bits(s(x))] = [8 0 0] [12]
[8 0 0] x + [15]
[8 0 0] [15]
> [8 0 0] [11]
[8 0 0] x + [10]
[8 0 0] [8]
= [s(bits(half(s(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:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, bits(0()) -> 0()
, bits(s(x)) -> s(bits(half(s(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:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, bits(0()) -> 0()
, bits(s(x)) -> s(bits(half(s(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:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, bits(0()) -> 0()
, bits(s(x)) -> s(bits(half(s(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:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, bits(0()) -> 0()
, bits(s(x)) -> s(bits(half(s(x)))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..