interpretations
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(perfectp) = {}, Uargs(s) = {}, Uargs(f) = {},
Uargs(minus) = {}, Uargs(if) = {3}, Uargs(le) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[perfectp](x1) = [2] x1 + [0]
[0] = [2]
[false] = [0]
[s](x1) = [1] x1 + [2]
[f](x1, x2, x3, x4) = [1] x1 + [3]
[true] = [0]
[minus](x1, x2) = [0]
[if](x1, x2, x3) = [1] x1 + [1] x3 + [0]
[le](x1, x2) = [0]
This order satisfies following ordering constraints
[perfectp(0())] = [4]
> [0]
= [false()]
[perfectp(s(x))] = [2] x + [4]
> [1] x + [3]
= [f(x, s(0()), s(x), s(x))]
[f(0(), y, 0(), u)] = [5]
> [0]
= [true()]
[f(0(), y, s(z), u)] = [5]
> [0]
= [false()]
[f(s(x), 0(), z, u)] = [1] x + [5]
> [1] x + [3]
= [f(x, u, minus(z, s(x)), u)]
[f(s(x), s(y), z, u)] = [1] x + [5]
> [1] x + [3]
= [if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))]
Hurray, we answered YES(?,O(n^1))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u)) }
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:
{ perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u)) }
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:
{ perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u)) }
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:
{ perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..