interpretations
YES(?,O(n^3))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).
Strict Trs:
{ f(a()) -> f(c(a()))
, f(a()) -> f(d(a()))
, f(c(X)) -> X
, f(c(a())) -> f(d(b()))
, f(c(b())) -> f(d(a()))
, f(d(X)) -> X
, e(g(X)) -> e(X) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^3))
The following argument positions are usable:
Uargs(f) = {}, Uargs(c) = {}, Uargs(d) = {}, Uargs(e) = {},
Uargs(g) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[3 1 1] [2]
[f](x1) = [2 0 2] x1 + [0]
[3 1 2] [2]
[3]
[a] = [2]
[1]
[0 1 0] [0]
[c](x1) = [1 0 0] x1 + [1]
[0 0 1] [0]
[0 0 0] [0]
[d](x1) = [1 0 1] x1 + [0]
[0 1 0] [2]
[2]
[b] = [1]
[3]
[1 0 0] [2]
[e](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[1 0 1] [2]
[g](x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
This order satisfies following ordering constraints
[f(a())] = [14]
[8]
[15]
> [13]
[6]
[14]
= [f(c(a()))]
[f(a())] = [14]
[8]
[15]
> [10]
[8]
[14]
= [f(d(a()))]
[f(c(X))] = [1 3 1] [3]
[0 2 2] X + [0]
[1 3 2] [3]
> [1 0 0] [0]
[0 1 0] X + [0]
[0 0 1] [0]
= [X]
[f(c(a()))] = [13]
[6]
[14]
> [10]
[6]
[13]
= [f(d(b()))]
[f(c(b()))] = [11]
[8]
[14]
> [10]
[8]
[14]
= [f(d(a()))]
[f(d(X))] = [1 1 1] [4]
[0 2 0] X + [4]
[1 2 1] [6]
> [1 0 0] [0]
[0 1 0] X + [0]
[0 0 1] [0]
= [X]
[e(g(X))] = [1 0 1] [4]
[0 0 0] X + [0]
[0 0 0] [0]
> [1 0 0] [2]
[0 0 0] X + [0]
[0 0 0] [0]
= [e(X)]
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(a()) -> f(c(a()))
, f(c(X)) -> X
, f(c(a())) -> f(d(b()))
, f(a()) -> f(d(a()))
, f(d(X)) -> X
, f(c(b())) -> f(d(a()))
, e(g(X)) -> e(X) }
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(a()) -> f(c(a()))
, f(c(X)) -> X
, f(c(a())) -> f(d(b()))
, f(a()) -> f(d(a()))
, f(d(X)) -> X
, f(c(b())) -> f(d(a()))
, e(g(X)) -> e(X) }
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(a()) -> f(c(a()))
, f(c(X)) -> X
, f(c(a())) -> f(d(b()))
, f(a()) -> f(d(a()))
, f(d(X)) -> X
, f(c(b())) -> f(d(a()))
, e(g(X)) -> e(X) }
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(a()) -> f(c(a()))
, f(c(X)) -> X
, f(c(a())) -> f(d(b()))
, f(a()) -> f(d(a()))
, f(d(X)) -> X
, f(c(b())) -> f(d(a()))
, e(g(X)) -> e(X) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..