interpretations
Execution Time (secs) | - |
Answer | YES(?,O(n^2)) |
Input | SK90 2.16 |
YES(?,O(n^2))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^2)).
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(x, s(x))
, g(0(), y) -> y
, g(s(x), y) -> g(x, s(+(y, x)))
, g(s(x), y) -> g(x, +(y, s(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^2))
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {1}, Uargs(g) = {2}, Uargs(+) = {}
TcT has computed following constructor-restricted polynomial
interpretation.
[f](x1) = x1^2
[0]() = 2
[1]() = 0
[s](x1) = 3 + x1
[g](x1, x2) = 3*x1 + x1^2 + 2*x2
[+](x1, x2) = x1 + 2*x2
This order satisfies following ordering constraints
[f(0())] = 4
>
= [1()]
[f(s(x))] = 9 + 6*x + x^2
> 5*x + x^2 + 6
= [g(x, s(x))]
[g(0(), y)] = 10 + 2*y
> y
= [y]
[g(s(x), y)] = 18 + 9*x + x^2 + 2*y
> 7*x + x^2 + 6 + 2*y
= [g(x, s(+(y, x)))]
[g(s(x), y)] = 18 + 9*x + x^2 + 2*y
> 7*x + x^2 + 2*y + 12
= [g(x, +(y, s(x)))]
[+(x, 0())] = x + 4
> x
= [x]
[+(x, s(y))] = x + 6 + 2*y
> 3 + x + 2*y
= [s(+(x, y))]
Hurray, we answered YES(?,O(n^2))
lmpo
Execution Time (secs) | - |
Answer | MAYBE |
Input | SK90 2.16 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(x, s(x))
, g(0(), y) -> y
, g(s(x), y) -> g(x, +(y, s(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, g(s(x), y) -> g(x, s(+(y, x))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
mpo
Execution Time (secs) | - |
Answer | MAYBE |
Input | SK90 2.16 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(x, s(x))
, g(0(), y) -> y
, g(s(x), y) -> g(x, +(y, s(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, g(s(x), y) -> g(x, s(+(y, x))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar
Execution Time (secs) | 0.149 |
Answer | MAYBE |
Input | SK90 2.16 |
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(x, s(x))
, g(0(), y) -> y
, g(s(x), y) -> g(x, +(y, s(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, g(s(x), y) -> g(x, s(+(y, x))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar-ps
Execution Time (secs) | 0.277 |
Answer | YES(?,POLY) |
Input | SK90 2.16 |
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(x, s(x))
, g(0(), y) -> y
, g(s(x), y) -> g(x, +(y, s(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, g(s(x), y) -> g(x, s(+(y, x))) }
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) = {}, safe(0) = {}, safe(1) = {}, safe(s) = {1},
safe(g) = {2}, safe(+) = {1}
and precedence
g > +, 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(0();) -> 1()
, f(s(; x);) -> g(x; s(; x))
, g(0(); y) -> y
, g(s(; x); y) -> g(x; +(s(; x); y))
, +(0(); x) -> x
, +(s(; y); x) -> s(; +(y; x))
, g(s(; x); y) -> g(x; s(; +(x; y))) }
Weak Trs :
Hurray, we answered YES(?,POLY)