interpretations
Execution Time (secs) | - |
Answer | YES(?,O(n^1)) |
Input | TCT 09 ma1 |
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(f) = {2}, Uargs(s) = {}, Uargs(g) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[f](x1, x2) = [1] x1 + [1] x2 + [1]
[s](x1) = [1] x1 + [3]
[g](x1, x2) = [1] x2 + [2]
[0] = [2]
This order satisfies following ordering constraints
[f(s(x), y)] = [1] x + [1] y + [4]
> [1] x + [1] y + [3]
= [f(x, g(x, y))]
[f(0(), y)] = [1] y + [3]
> [1] y + [0]
= [y]
[g(x, y)] = [1] y + [2]
> [1] y + [0]
= [y]
Hurray, we answered YES(?,O(n^1))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar
Execution Time (secs) | 0.093 |
Answer | MAYBE |
Input | TCT 09 ma1 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar-ps
Execution Time (secs) | 0.113 |
Answer | YES(?,POLY) |
Input | TCT 09 ma1 |
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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) = {2}, safe(s) = {1}, safe(g) = {1, 2}, safe(0) = {}
and precedence
f > g .
Following symbols are considered recursive:
{f, g}
The recursion depth is 2.
For your convenience, here are the oriented rules in predicative
notation, possibly applying argument filtering:
Strict DPs:
Weak DPs :
Strict Trs:
{ f(s(; x); y) -> f(x; g(; x, y))
, f(0(); y) -> y
, g(; x, y) -> y }
Weak Trs :
Hurray, we answered YES(?,POLY)