interpretations
Execution Time (secs) | - |
Answer | YES(?,O(n^1)) |
Input | SK90 2.54 |
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ f(x, a()) -> x
, f(x, g(y)) -> f(g(x), y) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[f](x1, x2) = [1] x1 + [2] x2 + [0]
[a] = [3]
[g](x1) = [1] x1 + [2]
This order satisfies following ordering constraints
[f(x, a())] = [1] x + [6]
> [1] x + [0]
= [x]
[f(x, g(y))] = [1] x + [2] y + [4]
> [1] x + [2] y + [2]
= [f(g(x), y)]
Hurray, we answered YES(?,O(n^1))
lmpo
Execution Time (secs) | - |
Answer | MAYBE |
Input | SK90 2.54 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(x, a()) -> x
, f(x, g(y)) -> f(g(x), y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
mpo
Execution Time (secs) | - |
Answer | MAYBE |
Input | SK90 2.54 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(x, a()) -> x
, f(x, g(y)) -> f(g(x), y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar
Execution Time (secs) | 0.043 |
Answer | MAYBE |
Input | SK90 2.54 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(x, a()) -> x
, f(x, g(y)) -> f(g(x), y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar-ps
Execution Time (secs) | 0.067 |
Answer | YES(?,POLY) |
Input | SK90 2.54 |
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ f(x, a()) -> x
, f(x, g(y)) -> f(g(x), y) }
Obligation:
innermost runtime complexity
Answer:
YES(?,POLY)
The input was oriented with the instance of 'Polynomial Path Order
(PS)' as induced by the safe mapping
safe(f) = {1}, safe(a) = {}, safe(g) = {1}
and precedence
empty .
Following symbols are considered recursive:
{f}
The recursion depth is 1.
For your convenience, here are the oriented rules in predicative
notation, possibly applying argument filtering:
Strict DPs:
Weak DPs :
Strict Trs:
{ f(a(); x) -> x
, f(g(; y); x) -> f(y; g(; x)) }
Weak Trs :
Hurray, we answered YES(?,POLY)