interpretations
YES(?,O(n^3))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).
Strict Trs:
{ f(s(X)) -> f(X)
, g(cons(s(X), Y)) -> s(X)
, g(cons(0(), Y)) -> g(Y)
, h(cons(X, Y)) -> h(g(cons(X, Y))) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(g) = {}, Uargs(cons) = {},
Uargs(h) = {1}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[1 0 1] [0]
[f](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[1 0 1] [1]
[s](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[1 1 3] [0]
[g](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[1 0 1] [1 1 3] [1]
[cons](x1, x2) = [0 1 0] x1 + [0 0 2] x2 + [3]
[0 0 0] [0 0 1] [2]
[2]
[0] = [0]
[3]
[1 2 2] [0]
[h](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
This order satisfies following ordering constraints
[f(s(X))] = [1 0 1] [1]
[0 0 0] X + [0]
[0 0 0] [0]
> [1 0 1] [0]
[0 0 0] X + [0]
[0 0 0] [0]
= [f(X)]
[g(cons(s(X), Y))] = [1 0 1] [1 1 8] [11]
[0 0 0] X + [0 0 0] Y + [0]
[0 0 0] [0 0 0] [0]
> [1 0 1] [1]
[0 0 0] X + [0]
[0 0 0] [0]
= [s(X)]
[g(cons(0(), Y))] = [1 1 8] [15]
[0 0 0] Y + [0]
[0 0 0] [0]
> [1 1 3] [0]
[0 0 0] Y + [0]
[0 0 0] [0]
= [g(Y)]
[h(cons(X, Y))] = [1 2 1] [1 1 9] [11]
[0 0 0] X + [0 0 0] Y + [0]
[0 0 0] [0 0 0] [0]
> [1 1 1] [1 1 8] [10]
[0 0 0] X + [0 0 0] Y + [0]
[0 0 0] [0 0 0] [0]
= [h(g(cons(X, Y)))]
Hurray, we answered YES(?,O(n^3))
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(s(X)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, 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)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, Y))) }
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:
{ f(s(X)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, Y))) }
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:
{ f(s(X)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, Y))) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..