interpretations
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ f(X, X) -> c(X)
, f(X, c(X)) -> f(s(X), X)
, f(s(X), X) -> f(X, a(X)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(a) = {}, Uargs(c) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[f](x1, x2) = [1] x1 + [1] x2 + [3]
[s](x1) = [1]
[a](x1) = [0]
[c](x1) = [2]
This order satisfies following ordering constraints
[f(X, X)] = [2] X + [3]
> [2]
= [c(X)]
[f(X, c(X))] = [1] X + [5]
> [1] X + [4]
= [f(s(X), X)]
[f(s(X), X)] = [1] X + [4]
> [1] X + [3]
= [f(X, a(X))]
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), X) -> f(X, a(X))
, f(X, c(X)) -> f(s(X), X)
, f(X, X) -> c(X) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
mpo
YES(?,PRIMREC)
We are left with following problem, upon which TcT provides the
certificate YES(?,PRIMREC).
Strict Trs:
{ f(s(X), X) -> f(X, a(X))
, f(X, c(X)) -> f(s(X), X)
, f(X, X) -> c(X) }
Obligation:
innermost runtime complexity
Answer:
YES(?,PRIMREC)
The input was oriented with the instance of'multiset path orders'
as induced by the precedence
f > c, s > a, c > s .
Hurray, we answered YES(?,PRIMREC)
popstar
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ f(s(X), X) -> f(X, a(X))
, f(X, c(X)) -> f(s(X), X)
, f(X, X) -> c(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(s(X), X) -> f(X, a(X))
, f(X, c(X)) -> f(s(X), X)
, f(X, X) -> c(X) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..