interpretations
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0() }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(g) = {}, Uargs(s) = {}, Uargs(f) = {1}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[g](x1) = [2] x1 + [0]
[0] = [2]
[s](x1) = [1] x1 + [2]
[f](x1) = [1] x1 + [3]
This order satisfies following ordering constraints
[g(0())] = [4]
> [2]
= [0()]
[g(s(x))] = [2] x + [4]
> [2] x + [3]
= [f(g(x))]
[f(0())] = [5]
> [2]
= [0()]
Hurray, we answered YES(?,O(n^1))
lmpo
YES(?,ELEMENTARY)
We are left with following problem, upon which TcT provides the
certificate YES(?,ELEMENTARY).
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0() }
Obligation:
innermost runtime complexity
Answer:
YES(?,ELEMENTARY)
The input was oriented with the instance of 'Lightweight Multiset
Path Order' as induced by the safe mapping
safe(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g, f}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0() }
Weak Trs :
Hurray, we answered YES(?,ELEMENTARY)
mpo
YES(?,PRIMREC)
We are left with following problem, upon which TcT provides the
certificate YES(?,PRIMREC).
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0() }
Obligation:
innermost runtime complexity
Answer:
YES(?,PRIMREC)
The input was oriented with the instance of'multiset path orders'
as induced by the precedence
s > g, s > f .
Hurray, we answered YES(?,PRIMREC)
popstar
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0() }
Obligation:
innermost runtime complexity
Answer:
YES(?,POLY)
The input was oriented with the instance of 'Polynomial Path Order'
as induced by the safe mapping
safe(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g, f}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0() }
Weak Trs :
Hurray, we answered YES(?,POLY)
popstar-ps
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0() }
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(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g, f}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0() }
Weak Trs :
Hurray, we answered YES(?,POLY)